The name Challah:
Bread in Hebrew is called Lechem while the separated dough is called Challah. It is customary to call the Shabbos bread Challah in order to serve as a reminder to women to separate Challah from the dough. In previous times it was common in many communities to refer to the Shabbos bread as “Barchas”. The reason for this is because these Challahs serve as a channel of blessing during the Shabbos meal.
Shape of the Challahs:
It is customary to form the Challahs for Shabbos as a long straight dough. This is opposed to round or square. The reason for this is because the Challahs represent the letter Vav of the Tetragrammaton. Alternatively the two Challahs in the shape of a Vav represent the twelve showbreads of the Temple, as Vav is Gematria of six.
Rosh Hashanah: The ancient custom of Ashkenazi Jewry is to bake round Challahs in honor of Rosh Hashanah. This symbolizing the roundness of a crown and corresponds to the coronation of Hashem on Rosh Hashana. Alternatively it is done as a symbol of good omen as all round items due to not have a start or finish and hence reflects a long life. Likewise round represents unity. Some write that this applies only on Rosh Hashanah itself, however on Shabbos Shuva one is to return to the accustomed shape of the two Vav’s.
Braid: It is customary to braid the Challahs baked for Shabbos as in the past it was common to add meat gravy to the dough and hence the Challah required a sign that would remind one not to eat it with dairy. This custom has remained today as well despite that the Challahs are left Pareve.
Placing the Challah on the table after baking:
Some Poskim record that the custom is to place the Challahs that will be eaten Friday night on the Shabbos table directly after removing them from the oven, and that doing so is included within Kavod Shabbos. This is not the current widespread custom. Nevertheless it is proper to do so.
 Ashel Avraham [Butchach] 260
 Piskeiy Teshuvos 243 footnote 88
 Elya Raba 167/2 in name of Shlah. The five fingers on each hand which holds the Challahs represent the two Heis of the Tetragrammaton, and the Challahs form a Yud when held. Hence the Vav of the shape of the Challah complete the Tetragrammaton. [Shem Havayah]. [ibid]
 Likkutei Mahrich in name of Divrei Chaim
 Piskeiy Teshuvos 583 footnote 46; 242 footnote 105; Oatzer Minhagei Chabad 129
 Brought in Piskeiy Teshuvos 583 footnote 46
 P”M 242 M”Z 1; See Yoreh Deah 97/1; “A Semicha Aid for the Laws of Basar Bechalav” Chapter 97
 Taz Yoreh Deah 178/7; Chasam Sofer in his glosses on 242
 This is similar to the showbread which was placed directly on the table after it was baked. [Divrei Yisrael 2 p. 30]
 Likkutei Mahrich
 Piskeiy Teshuvos 242/11