Zevachim 98 - What Each Kohen is Entitled to
The priests's portions include the meat and hide of the most holy offerings, the flour offerings, and the breast and the right thigh from the thanksgiving and peace offerings.
Basically, every kohen is entitled to a share from every sacrifice. However, practically it would be inconvenient for everyone to come to the Temple when they pleased, so Moses diveded them into eight groups, and later Shmuel and David expanded this to twenty four groups, or families. Therefore, each kohen would have to serve in the Temple for one week in six months, and during this week he was entitled to a share from sacrifices.
If a kohen became ritually impure and went to the mikveh to dip in order to purify himself, he still needs to wait for sun to go down, after which he becomes completely pure and can eat sacrifices. During that day he is still partially impure, and has no claim to the sacrifices slaughtered on that day, even though he will be fit to eat them in the evening. The same is true for a kohen who needs to offer additional sacrifices for his purification - he cannot take a raincheck to apply it in the evening.
Art: Albert Bierstadt - Sundown at Yosemite