Obligation to answer Amen:
A. The greatness and the obligation:
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].
Whoever answers Amen is greater than even the person who said the blessing. The reason for this is because in the word Amen is hinted two names of Hashem, both Adniy and Havayah. Alternatively, the reason is because answering Amen includes three Mitzvos: Shavua, Kabala and Emuna.
One who hears a blessing and does not answer Amen, his punishment is very great.
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 his 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 1000’s prior to the period of the Rhineland 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
 The reason: This is learned from the verse “Ki Shem Hashem Ekra, Havu Godel Lelokeinu”. Moshe said to Bnei Yisarel 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
 Shabbos 119b
 Gemara ibid; Rabbeinu Yona Brachos “Some people’s concentration are aroused through raising their voice.”
 Rashi ibid
 Brachos 53b
 Sefer Chassidim 19
 Elya Raba 124/11; Perisha 124; This means that he is accepting the blessing with a swear and faith. See Chasam Sofer 15
 Chayeh Adam 6/1
 Nehara Hashaleim p. 15, brought in Kaf Hachaim 124/30