“And this shall be the law of the Priests from the people… and he shall give to the priest the forearm, cheeks and stomach!” (Devarim 18:3)
It is a positive commandment to all of the members of Klal Yisrael when they slaughter a Kosher animal that they must give the right foreleg, the cheeks and the stomach to the priest, as it says “And this shall be the law of the Priests from the people… and he shall give to the priest the forearm, cheeks and stomach!”. Chazal said that the reason for this commandment is that in the merit of their ancestor Pinchas, who took the vengeance of Hashem in the matter of Kozbi the daughter of Tzur, and endangered his own life to sanctify the Name of Hashem when he killed a prince of a tribe of Klal Yisrael, his descendants the priests merited to forever receive this present from Hashem. The foreleg represents the “And he took a spear”. The cheeks are in the merit of the fact that he prayed about the pain of Klal Yisrael, as it says “And Pinchas stood and prayed!”. The stomach represents the “And the woman into her stomach!”. We learn from this that part of the reward of one who sanctifies the Name of Hashem in public is that he and his descendants receive reward in this world, apart from the reward that he receives in the next.
This commandment applies to regular animals, but not to offerings. It applies to Jewish men and women, but not to the priests. It is unclear whether the Levites are obligated to fulfil this commandment. They therefore do not give these parts but if a Priest took them he is not obligated to return them.
The commentators disagree as to whether these presents apply nowadays. It would appear that the conclusion is that they do apply, but that we cannot force the butchers to give them to the Priests.
A Jew who slaughters an animal and does not give these presents to the Priest, has transgressed this commandment. If there is no Priest or Priestess available, and if he waits until he finds a Priest the meat will go bad, he may evaluate them and eat them and give their worth to any Priest that he wants.