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.[1] Alternatively the two Challahs in the shape of a Vav represent the twelve showbreads of the Temple, as Vav is Gemtria of six.[2]

Rosh Hashanah:[3] 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 longevity of life. Likewise round represents unity. Some[4] write that this applies only on Rosh Hashanah itself, however on Shabbos Shuva one is to return to the accustomed shape of the two Vavs.

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.[5] This custom has remained today as well despite that the Challahs are left Pareve.

___________________________________________________________

[1] Elya Raba 167:2 in name of Shlah. The five fingers on each hand which holds the Challahs represent the two Heis of the Tetragramottan, and the Challahs form a Yud when held. Hnece the Vav of the shape of the Challah complete the Tetragramottan. [Shem Havayah]. [ibid]

[2] Likutei Mahrich in name of Divrei Chaim

[3] Piskeiy Teshuvos 583 footnote 46; 242 footnote 105; Otzar Minhagei Chabad 129

[4] Brought in Piskeiy Teshuvos 583 footnote 46

[5] P”M 242 M”Z 1; See Yoreh Deah 97:1; “A Semicha Aid for the Laws of Basar Bechalav” Chapter 97