The greatness and obligation of answering Amen:
It is an obligation to answer Amen towards the blessing said by a Jew. This applies even if the person who hears the blessing is not obligated in this blessing at all.
The meaning: The word Amen is an acronym for the words Keil Melech Neman, [which means that Hashem is a trustworthy king and will fulfill the blessing]. Amen is an expression of belief coming from the word Hamanas Devarim [i.e. Emuna].
The intent required when answering Amen: The intent that one is to have in mind upon answering Amen is that the blessing that the person said is true and I believe in this. This intent however is only applicable by those blessings that are factual statements of Hashem’s greatness [such as Baruch Sheamar, Yishtabach, and Goal Yisrael]. However, those statements that are a request and appeal towards Hashem, such as the stanzas of Kaddish [which is a request that Hashem return his Shechina] and the like, one is to intend on the future, that the words will come true and his request will be speedily fulfilled. By those statements that are both admiration and praise and also hope and anticipation that the words being said will be speedily fulfilled, it is proper to intend in the Amen both interpretations; that the statement said is true and that his words will come true and it will be speedily fulfilled. An example of such blessings are the middle blessings of Chazaras Hashatz, as well as the blessings of Ritzei and Sim Shalom.
Amen to a blessing that does not include Hashem’s name: Whoever blesses another Jew it is a Mitzvah to answer Amen to his blessing. [This applies even though Hashem’s name is not mentioned in the blessing, such as by a Mi Shebeirach, or Harachaman, or a personal blessing given by a friend and the like. An example of this would be for a mourner to answer Amen towards a comforter parting remarks of consolement. One is however not to answer Amen to a blessing that is said without Hashem’s name because of a doubt, such as the blessing of Baruch Patrani Meonsho Shel Zeh.]
One who hears a blessing and does not answer Amen, his punishment is very great.
The greatness-Answering Amen is in one aspect even greater than saying the blessing:
Whoever answers Amen is [in one aspect] even greater than the person who said the blessing. Accordingly, we rule that whoever stole a Mitzvah and its blessing from another, a fine is not given if the “owner” was able to answer Amen. On the other hand, regarding another aspect, the person who says the blessing is greater than the person who says Amen. Thus, the reward of one who says the blessing and one who answers Amen is equal. Nevertheless, Hashem hastens the reward of one who says the blessing more than one who answers Amen. Accordingly, we rule that if a person has the choice between saying the blessing or answering Amen he should choose to say the blessing.
The reasons for its greatness: The reason Amen holds an advantage over the blessing is because the Amen is the finalization of the blessing, and is similar to the last warrior who won the battle. The Amen helps make the blessing become effective and draw down its Divine request. The Amen destroys any prosecuting angels who prevent the blessing from becoming true. It also banishes the forces of evil from nurturing from the blessing. A blessing is similar to an unnotarized document, and the Amen is like a notary to the blessing that it will take place. The Amen is the second witness, who joins the first witness which is the person saying the blessing, to authenticate the blessing. Alternatively, the reason is because one who hears a blessing is as if he said it, and since in addition he answers Amen, he is therefore greater than the person who said the blessing who may not say Amen. Alternatively, the reason is because in the word Amen is hinted two names of Hashem, both Adnai and Havayah. Alternatively, the reason is because answering Amen includes three Mitzvos: Shavua, Kabala and Emuna.
Rav Mordechai Jaffe, the author of the Levushim, once visited his teacher Rabbi Abuhav to study from him the laws of the Ibur, of sanctifying the new moon. While there, Rav Abuhav’s son said a blessing over a fruit aloud and everyone in the family answered Amen to his blessing. Unintentionally, being over-engrossed in his studies, Rabbi Jaffe did not answer Amen to the blessing. His teacher Rabbi Abuhav became extremely angry at his student and severely admonished him, going to the extent of placing him in excommunication. Rav Jaffe had to leave his teachers home and pleaded to his teacher to accept him back. Several days passed and his teacher’s wrath still did not settle, and he did not agree to forgive his student despite the constant implorations. He asked his teacher why he is deserving of such severe consequences when seemingly he committed an unintentional minor transgression. His teacher replied to him “In truth I love you very much, even more than my children, although you should know that when you did not answer Amen you became liable for death from Heaven, and I needed to nullify this decree through admonishing you and causing you distance and pain. I forgive you now with a full heart. Let me tell you a story that happened in the 1600’s prior to the period of the Chmielnicki massacres. There was a certain pious Jew who heard his son say a blessing over bread and did not answer Amen, and it was decreed upon him to die. This Jew was later informed on to the government and was killed shortly thereafter.”
 Admur 215:2; Michaber 215:2; Mishneh Brachos 51b; See Yesod Veshoresh Havoda 5:6 for the greatness and importance of answering Amen
 The reason: This is learned from the verse “Ki Shem Hashem Ekra, Havu Godel Lelokeinu”. Moshe said to Bnei Yisrael that when he recites a blessing with Hashem’s name, the listeners are to answer Amen and give praise to Hashem. [M”B 215:8]
 Admur 124:11; 61:4; Levush 124:4
 Admur 124:9; Tur 124
 Admur 124:9
 Admur ibid; Michaber 124:6; Tur 124; Abudarham
 M”A 124:10
 Admur ibid; M”A ibid
 Admur ibid; Taz 124:3; M”A ibid
 Admur 189:6; M”A 215:3 in name of Midrash; Chesed Lealafim 215:4; Kaf Hachaim 215:11
 Admur ibid
Is this a Mitzvah or obligation? From the wording of Admur ibid it is implied that it is not an obligation but a Midas Chassidus and so is also implied from Orchos Chaim Kerias Hatorah 3 who says “It is permitted to answer Amen” and so rules Emek Sheila 53:2. However, some Poskim rule it is an obligation to answer Amen to a prayer or blessing, such as Harachaman. [M”A 215:3 in name of Midrash; Chesed Lealafim 215:4; Kaf Hachaim 215:11]
 See Aruch Hashulchan 215:1; Kaf Hachaim ibid; Piskeiy Teshuvos 215:7 footnote 42
 Toras Menachem 1988 2:245 and 597 [printed in Shulchan Menachem 5:280] that this especially applies to the blessing said to an Avel; Rav SZ”A, brought in Pnei Baruch ibid; Nitei Gavriel 90:2; Piskeiy Teshuvos ibid
 Betzeil Hachochmah 5:90
 Shabbos 119b
 Gemara ibid; Rabbeinu Yona Brachos “Some people’s concentration are aroused through raising their voice.”
 Rashi ibid
 Chayeh Adam 6:1
 See Shach C.M. 382:7; Shaareiy Teshuvah 215:2; Likkutei Sichos 35:216-22; See Yesod Veshoresh Havoda 5:6 for the greatness and importance of answering Amen
Background: There is an apparent dispute in the Talmud [Brachos 53b; Nazir 66b] as to what is greater; the Amen or the blessing. Each side of the argument seemingly carries a practical ramification in which they would dispute [regarding fine for stolen blessing, and regarding if one should try to lead Zimun]. The Shulchan Aruch in different areas ruled on these ramifications in a seemingly contradictory way. The Poskim [M”A 201:6; Shach C.M. 382:7] who answered this contradiction conclude that Amen is equal to the blessing, but not greater, and therefore the two rulings in Shulchan Aruch stand true, and the final stance is unlike the opinion who says Amen is greater. The Rebbe in Likkutei Sichos 35:216-22 however takes an approach that in truth Amen is greater in one aspect and less great in another and therefore they equal out in reward.
Practical ramification-One who stole a blessing: The practical ramification in whether we say that one who answers Amen is greater than the person who said the blessing is regarding if one stole a blessing from another, such as someone else covered the blood of a bird, must the stealer pay the “owner” ten Zehuvim if the answered, or person could have answered, Amen. Practically, we rule that he is not obligated to pay being that answering Amen is even greater than the blessing. [Rama 382:1; Shach C.M. 382:4 [see there in great length]; Rosh in Chulin end of Perek Kisuiy Hadam in name of Rabbeinu Tam; Mordechai Chulin 655; Tur Y.D. 28; Smeh C.M. 382:7]
Practical ramification-Leading the Zimun: We rule that it is a Mitzvah to lead the Zimun and say the blessing over the Kos Shel Bracha. [Brachos 53b; Nazir 66b-end; Michaber 201:4; Admur 201:5] This implies that we do not rule like the statement in Brachos that answering Amen is greater than saying the blessing. [Simple implication of Gemara ibid that this matter is a dispute, and only according to the opinion who says it is not greater do we hold that one should lead the Zimun; Ravaya Brachos ibid; Piskei Harid Brachos ibid; Kesef Mishneh in opinion of Rambam Brachos 1:11] This contradicts the previous ruling regarding not giving a fine to one who stole a blessing. [M”A 201:6; Madanei Yom Tov on Rosh Chulin 6:8, brought in Shach C.M. 382:7] Some therefore answer that even the opposing opinion agrees that one who answers Amen gets rewarded, and that is why a fine is not given, and not because answering Amen is greater. [M”A ibid; Shach ibid; See Shaareiy Teshuvah 215:2; Panim Meiros 1:57; Birkeiy Yosef 215] Others answer that in truth everyone agrees that there is an aspect of advantage for the Amen over the blessing and an advantage of a quicker reward for the blessing over the Amen and therefore their reward is equal. [Madanei Yom Tov; Likkutei Sichos ibid p. 217]
 Madanei Yom Tov on Rosh Chulin 6:8; Likkutei Sichos 35:216-22 in answer of contradiction brought in coming footnotes
The reason: As he completes the blessing. This is the advantage of Poel over Koach. However, the person who said the blessing is greater in the fact that he started the blessing. [See reasons and coming footnotes and Likkutei Sichos ibid in great length on this subject]
 Brachos 53b; Nazir 66b; Shach C.M. 382:4 in initial explanation [see there in great length and his later explanation]; Tur Y.D. 28; Smeh C.M. 382:7; Levush 215, brought in Shaareiy Teshuvah 215:2; Rosh in Chulin end of Perek Kisuiy Hadam in name of Rabbeinu Tam regarding a stolen blessing; Mordechai Chulin 655; Implication of Semag Aseh 27; Orchos Chaim Dinei Amen; Rashal Hachovel 60; P”M 124 M”Z 4 “So we rule”; See Likkutei Sichos 35:216-22 in great length on this subject!
Other opinions: Some Poskim rule that although the Gemara makes the above statement, nevertheless it is not the final Halachic ruling, and rather we hold like the other opinion in the Gemara ibid that one who answers Amen is equal to one who says the blessing in reward, although Hashem hastens the reward for the person who said the blessing. [M”A 201:6; Shach C.M. 382:4 in later explanation; See Shaareiy Yosef 7 in name of Ritva, brought in Shaareiy Teshuvah 215:2; Panim Meiros 1:57; Birkeiy Yosef 215] See Likkutei Sichos ibid who answers the apparent contradictions and conflicting opinions
 Initial explanation in Shach C.M. 382:4 [see there in great length]; Rosh in Chulin end of Perek Kisuiy Hadam in name of Rabbeinu Tam; Mordechai Chulin 655; Tur Y.D. 28; Smeh C.M. 382:7; Likkutei Sichos ibid
Other opinions: Some Poskim rule that nevertheless a fine is imposed for the stolen Mitzvah. [Rashal Hachovel 60, brought in Shach ibid and negated by him] Some Poskim rule that this Halacha has nothing to do with the above statement of “Amen being greater than the blessing” as even the opposing opinion agrees that one who answers Amen gets rewarded equal, and that is why a fine is not given. [M”A 201:6; Later explanation in Shach C.M. 382:7; See Likkutei Sichos ibid who negates this explanation]
 Likkutei Sichos ibid in answer of contradiction brought in previous footnotes
The reason: As he started the blessing. This is the advantage of Koach over Poel. [ibid]
 M”A 201:6; Shach C.M. 382:7; Brachos 53b; Nazir 66b-end; Likkutei Sichos ibid
 Admur 201:5; Brachos 53b; Nazir 66b-end
 Admur 201:5; Michaber 201:4; Brachos 53b; Nazir 66b-end
 Admur 167:3; Rama 167:2; Darkei Moshe 167:4; Or Zarua based on Yerushalmi; Rosh end of Nazir; Gra 167
 Rebbe Nihoraiy in Brachos 53b and Nazir 66b as explained in Tosafus ibid
 Maharsha Nazir 66b; Likkutei Sichos ibid p. 220; Thus we rule that the person saying the blessing must concentrate on the Amen of the listener. [Admur 167:14; Rama 167:2; Or Zarua 1:102 and 178 based on Yerushalmi Brachos 7:3; P”M 167 A”A 36; Likkutei Sichos 35 p. 220] Furthermore, we find Poskim who rule that if the listener did not say Amen then neither the person who said the blessing or listener fulfill their obligation! [Or Zarua 1:102 and 178, brought in Darkei Moshe 167:4] We do not rule this way. [Darkei Moshe ibid; Likkutei Sichos ibid footnote 44]
 Or Hatorah Bereishis 3:566
 Orchos Chaim Din Aniyas Amen; Abudarham Seder Shacharis Shel Chol; See Zohar p. 229 and 271; Rokeiach 330;
 Rabbeinu Bechayeh Beshalach 14:31
 Perisha 124; See Admur 201:5; Likkutei Sichos ibid p. 218-219 who negates this explanation of Gemara
 Sefer Chassidim 19
 Shavuos 36a; Elya Raba 124:11; Perisha 124; This means that he is accepting the blessing with a swear and faith. See Chasam Sofer 15; See Likkutei Sichos ibid p. 219
 Nehara Hashaleim p. 15, brought in Kaf Hachaim 124:30; Vetzaruch Iyun as explained in Poskim that during learning one is exempt from answering.