There are multiple origins and meanings for the name:
1. Arabic (أبي) and Hebrew (אבי) name-giving - "daddy (Av), dad; proud", see the name Abu
2. Diminutive form of the given name Abraham or of Abel or of Aviel - "God (El) is my father (Av)"
3. Persian given name (ابی) meaning - "blue, watery"
4. Turkish (Turkic) first name, meaning - "older brother"
May also refer to Abi (feminine name ).