Under the Law of Moses, God gave strict rules that only a Levite priest’s family could eat from the sacrifices offered by Israel as prescribed by the Law.
As we have observed, sacrifice is a consequence of sin that goes back to Adam and Eve, Cain and Abel. Under the Law of Moses, the Israelites were instructed to give numerous types of sacrifices and offerings, of which, portions of some types were to be eaten by the priest and his household.
GOD wanted to ensure that the sacrifices and offerings were eaten by the individuals He was providing for, so He told Moses the following:
10 No foreigner shall eat the holy things; one who sojourns with the priest or a hired servant shall not eat the holy things. 11 But if the priest buys a soul with his money, this one may eat the priest’s food; and one who is born in his house may eat his food. 12 If the priest’s daughter is married to a foreigner, she may not eat of the holy offerings. 13 But if the priest’s daughter is a widow or divorced and has no child, and has returned to her father’s house as in her youth, she may eat her father’s food; but no foreigner shall eat it. 14 Also, if a man eats the holy things in ignorance, then he shall restore the holy thing to the priest and add one-fifth to it. 15 They shall not defile the holy things of the children of Israel, which they offer to the Lord, 16 or allow them to bear the guilt of trespass when they eat their holy things; for I the Lord sanctify them.’”Leviticus 22:10-16 OSB
Why was this important to GOD?
The sacrifices were holy because GOD prescribed them for a specific purpose and the offerings themselves had gone through sanctification procedures (that GOD had set up and decided were acceptable to Himself).
Those procedures transfer the mundane common piece of bloody, dead meat, for example, into a holy, pleasing aroma offering, rising up to GOD.
Before a priest could begin their service that day to receive any offerings (and thus their individual portion of those sacrifices), the priest had to first complete a washing sanctification ritual, including putting on the priestly garments.
Having been purified themselves, once a sacrifice passed from the Israelite to the priest, the offering itself became holy. The offering had to remain holy for its duration (until it was consumed, whether by fire or by eating).
In GOD’s sight, the priest’s family was apparently considered holy (sanctified) as an extension of the priest’s sanctification. Thus, it was acceptable for the immediate family members in the priest’s house to eat the food offered to the priest.
But one who was outside of the priest’s household, such as the daughter who married a foreigner or a foreigner who is visiting, they would not have been seen by GOD as sanctified on behalf of the priest’s performance. For this reason, if they ate the sacred offering, it would be seen as sinful.