There are multiple origins and meanings for the name:
1. Diminutive form of the given name Gabriel - "strong man of God (El)" or of Gaylord - "cheerful, livery man"
2. Comes from the Old French word gai meaning - "cheerful, gay, merry, happy, jolly, cheery, bright, joyful, joyous, glad"
3. Hebrew given name (גיא) meaning - "valley, ravine, gorge, gulch, glen"
4. Greek name, meaning - "earthborn, born by Gaia (earth)"
May also refer to Gay (feminine name).