Non-kohanim were not allowed to eat the special portions given to the kohanim, including terumah and bikkurim (first fruits).
The kohein was allowed to use terumah to feed the members of his household. This included any non-Jewish slave he may have purchased or the child of a slave born in his home. These are considered members of his family for the purposes of terumah. But an indentured Jew who works a limited number of years – even one who has signed on to stay until the next Jubilee year – is not considered a permanent member of the household for this purpose as he will be leaving after a certain amount of time.
As we said in the previous mitzvah, the reason for this is that terumah is a special gift to the kohein given in exchange for his service in the Temple. It’s “members only” and may only be eaten by the permanent members of a kohein’s household. (Yes, a kohein’s daughter might later marry a non-kohein or a purchased slave might be freed but the indentured servant by definition is “just passing through.”)
This mitzvah applies to all non-kohanim when the laws of terumah are in effect. It is discussed in the Mishna in the first chapter of tractate Challah. It is codified in the Mishneh Torah in the sixth and in the eighth through tenth chapters of Hilchos Terumos. This mitzvah is #134 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.