What is "heave offering"

Heave offering \Heave" of`fer*ing\ (Jewish Antiq.) An offering or oblation heaved up or elevated before the altar, as the shoulder of the peace offering. See Wave offering.
--Ex. xxix. 27.

A heave offering, or terumah , plural teramot, is a kind of offering. The word is generally used in the positive sense of an offering to God, although sometimes it is also used in a negative sense, such as the ish teramot, a "[dishonest] judge who loves gifts".

In Chazalic literature it is listed as one of the twenty-four priestly gifts. The consumption of terumah is restricted by numerous Torah-based rules and could be eaten by priests, their families, and their servants. The terumah may be consumed only in a state of ritual purity.

This is also called the "great offering" (Hebrew terumah gedolah תרומה גדולה) which is, usually, a food item given to the Jewish priest, as a gift. The thirteenth-century French rabbi Hezekiah ben Manoah explains the adjective "great" (Hebrew gedolah) to be because this terumah is the first of all tithes given on produce and thus is given from the "greatest quantity of produce" before any other gift is given.