A. The pure, simple, unadorned word “Challah” means “a loaf of bread.” However, in Halachic terms, the word Challah has a very specific definition, and colloquially, it came to mean a certain type of bread thousands of years later.
B. The Halachic definition of Challah is a reference to Positive Mitzvah #133. It entails separating a section of dough from your kneadings and giving it to the kohen. This piece of dough is called "Challah." Any dough which is made of wheat, barley, spelt, oat or rye is obligated in this Mitzvah. The kohen and his family would eat the Challah while in a state of ritual purity. The Rabbis determined that the the home-baker give 1/24th of the dough to the kohen, while the commercial baker has to donate 1/48th of his dough.
C. Biblically speaking, the Mitzvah of Challah is only observed in the land of Israel. Furthermore, according to most Halachic authorities, the Mitzvah of Challah was a requirement only in the times of the Temple. Today, no Temple, no Challah. But the Rabbis re-instituted the practice of Challah -- even outside the land of Israel -- to commemorate this special Mitzvah. However, since today we are all considered ritually impure, the kohen cannot eat the Challah. Instead, Jewish women through the centuries knead homemade dough and then separate a piece of the dough and burn it. All kosher bakeries so the same -- they separate a piece of dough from each batch, and throw it on the floor of the oven. Today, only a small piece of dough is separated for Challah -- since the Challah isn't eaten, it would be wasteful to separate 1/24th or 1/48th of the dough.
D. Before separating the "Challah," the following blessing is recited:
Baruch atta Ado-noy Elo-hai-nu Melech ha'olam asher kid-e-sha-nu b'mitz-vo-tav v'tzi-vanu li-haf-rish Challah.
[Blessed are you, Lord our G-d, King of the universe, who has sanctified us with His commandments, and commanded us to separate Challah.]
E. Eventually, the soft, sweet bread loaves customarily eaten by the Shabbat meals became known as Challah (not “hally,” as per popular pronunciation).