What are heave-offerings?

Answer 1

1) Terumah, that portion of grain given to the Kohanim, is sometimes translated as a "heave-offering," since "terumah" literally means to lift up.

2) Certain offerings were ritually waved (וה×?×™×£ אותו הכהן) in the Holy Temple. These may more correctly (than Terumah) be called "heave-offerings," though the translation of "wave-offerings" is more clear.