Deuteronomy 18:3 "And this shall be the priests' portion from the people"

The priests dedicate their life to the service of HaShem in the Beit HaMikdash. It is proper for the people, whom they represent and benefit, to supply them with their needs.

In addition to the portions they receive from the sacrifices, this Positive Mitzvah commands us to give the priest certain portions of every animal slaughtered.