"The first of your kneading you shall set aside as a portion... to
Hashem." (Bemidbar 15:20)
In the time of the Beis Hamikdash, a portion of dough, called challah, was
separated from dough made from flour that was equal in volume to 43.2 eggs
(about five pounds of flour) and given to a kohein. In commemoration of
this, anyone making a dough of this size today must separate a small piece
of dough and burn it.
In the days of the Beis Hamikdash, when we were able to maintain purity,
kohanim were able to eat the challah portion given to them. Thus, the
kohein received all of his needs - bread, meat, clothing, money, and fruit
(from terumah) - from all of these mitzvos. Nowadays, we burn the
challah, symbolically reminding ourselves that this portion goes back to
Hashem in gratitude for His providing us with all of our needs (Sefer
HaChinuch, mitzvah 385).