You are to have the part of the most holy offerings that is kept
from the fire. From all the gifts they bring me as most holy offerings, whether
grain or sin or guilt offerings, that part belongs to you and your
sons. Eat it as something most holy; every male shall eat
it. You must regard it as holy. Numbers 18:9-10
The consumption
of the offering was twofold. One, it fed
the priests and their families who lived off the offerings. The second reason was more spiritual, as the
priest got rid of the sin the sacrifice represented and absorbed it into
themselves.
Jesus, as
the high priest, absorbed our sins into himself and died because of them and
for us. The priest at the time of Moses
symbolically represented the future Messiah who would do this once and for all.