Q. It appears to be universally Jewish to make braided challos for Shabbos. Since all authentic Jewish customs have deep roots and have been started by great people and deep thinkers, what is the intent or the connection to Shabbos of braided challos?
We thought of Hashem’s braiding of Chava’s hair on Erev Shabbos, but could not think of any causation between the two subjects, just correlation.

A. Sefer Aguda (Baba Kama 7: 102) counts as one of Ezra’s enactments, that women should bake early on Erev Shabbos.
Minhagei Betzias Lechem Mishna (p. 11, 12, 13 – Chaye Moshe p. 8 – Nitei Gavriel, YomTov 2: 7: n. 10)) explain that the form of the challos, is based on a teaching of the Arizal. He maintained one should bake twelve challos representing the lechem happonim. These twelve are divided into two distinct groups of six as was the showbread. Quoting Sidur Iyun Tefila (ibid. n. 28), he further elucidates that each chala should be braided from six different rolls of dough, thus representing the six breads of lechem happonim, that similarly were grouped and framed on each pile or set on the Showbread Table.
Chabad.Org provides the following reason for braiding challos; “Shabbat represents the idea of unity. The six days of the week are the paradigm of diversity. They are like the six directions in our three-dimensional world—north, south, west, east, up and down. During these days we are in a search outward, full of action and initiative, trying to master our environment.
Shabbat, on the other hand, represents the inner point. Shabbat points inward, and is full of the unity and the peace that comes with unity. That is why we greet one another with “Shabbat Shalom,” Shabbat of peace and unity. Shabbat also represents the innerness of absorbing the blessing from the six workdays and directing them to our homes and our lives.
Perhaps the braiding of the challah, which is eaten at the Shabbat table, also represents this idea of unity: how we tie everything together, bringing all the diversity in our lives together for a peaceful harmony and unity that only the Shabbat can achieve.”
Another reason mentioned for those who plait only three braids. (Ohr Sameach – ohr.edu) “The three braids are symbolic of the commands to observe Shabbat that appear in the Ten Commandments One braid represents the word “Zachor” – “Remember.” A second braid represents the word “Shamor” – “Guard.” The third braid is for “b’Dibbur Echad” – that these commands of “Remember” and “Guard” were said by G-d simultaneously and as one unit.”
Horav Shlomo Miller Shlit’a hinted that there may be more reasons. He mentioned that his parents had a minhag to bake challos on Hoshana Rabbah and Erev Yom Kippur, that resembled the crossed hands and spread fingers of a cohen in blessing.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a