Answer:
   
   Challah means dough and refers to bread made from dough that has
   undergone separation. There is a mitzvah (religious law) that requires
   the head of the dough to be separated and given to the priests as
   tithe. Since the destruction of the Temple, this mitzvah has been
   satisfied by separating a portion of the Challah (a piece about the
   size of an olive) and burning the separated piece in the oven. The
   preference is separate the dough before baking but it may be done
   after. Burning the separated piece is a symbolic sacrifice. Only
   breads made from wheat, barley, maize, spelt,and oats require
   separation.
   
   Challahs are normally eaten on the Sabbath (Shabbos). The five grains
   mentioned above were beyond the economic means of many of our
   ancestors, i.e., considered "rich man's food." Further, "egg" bread is
   considered to be richer bread than plain white bread. To make us all
   rich on Shabbos, we eat Challah. Challahs are always served in pairs
   on Shabbos and Yom Tovs (Holidays). This is symbolic of the showbreads
   of the Temple and the double portions of manna received in the desert
   on Friday. None was received on Shabbos.
   
   With respect to the braiding, there are several reasons. The three
   braids are symbolic of the commands to observe Shabbat that appear in
   the Ten Commandnments 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.
   
   Another reason is that Shabbat signifies and reminds us of three
   different concepts: The Creation of the World, the Exodus from Egypt
   and the Messianic Era. This is also the reason for three distinct
   separate Amidot - Silent Prayers - on Shabbat, as opposed to the
   weekday Amidah which is of identical wording three times a day (the
   theme of the fourth prayer of Shabbat - Mussaf ("additional") is said
   for the additional Temple sacrifice for Shabbat, and also applies on
   Festivals.) This idea also provides an understanding for the three
   meals eaten on Shabbat.
   
   For the most strictly observant, even the way the challah is cut is
   symbolic: Although the knife is on the table, it is not used, as the
   Bible recounts that the patriarch Abraham, tested by God, did not use
   the knife on his son Isaac. Instead the bread is torn after the
   blessing is said.
   
   On Rosh Hashana, the braided form is not used; instead, a round
   Challah, often with raisins for extra sweetness, is used. In its round
   form, the challah represents the cycle of life and the wholeness of
   the universe, and the seeds symbolize fertility and plenty.
   
   In some Jewish communities, holiday challah is also shaped like
   ladders and hands: the ladder to help us reach great heights and the
   hand as a symbol of the desire to be inscribed in the book of life for
   the coming year. (Some also believe it is an amulet against the evil
   eye.) Among Jews originating from Tripoli, it is customary,
   particularly on the New Year, to make challah with caraway seeds, a
   symbol of fertility. Among Moroccans, challah is made with raisins,
   nuts and anise in the dough and served with a hard-boiled egg placed
   on top. These are all symbols of sweetness and fertility. Many Central
   European Jews also add raisins to their challah dough and serve it
   with a little bowl of honey in the center.