1. to be surrounded, controlled.
2. to be fond of, desired, to be liked.
3. to be deceived or deluded.
5. head cold.
6. a kind of coconut.
Actually if you look up the word puni you will see the translations of 1-4 above. Punia is actually the passive/imperative form of puni (this probably makes more sense to the advanced language learners). ʻIa is usually the passive marker (peku = to kicked; peku ʻia - to be kicked). But with punia, it's a combination of puni + ʻia. There are some other Hawaiian words similar to this.
Punia is not used very often in spoken Hawaiian but is found more often in song, poetry, and older literature. Here are some examples:
Ke ʻala o ka lauaʻe, punia ai ka nahele - the fragrance of the laua'e fern permeates the forest.
Aloha wale ku'u kaikunāne ē, ua punia au - Alas for my brother, I am overcome with grief.
Punia kuʻu lei i ke ʻala o ke aloha - My beloved is surrounded by the sweet scent of love.