1. A nickname for "Luigi": This is the most common meaning. It's a familiar and affectionate nickname for the male name Luigi.
2. A slang term for "grandmother": This meaning is less common, but it exists in some regions of Italy.
Therefore, the meaning of "Gigi" depends on the context. If you see it used in a name, it likely means Luigi. If it's used in a conversation, it could mean either Luigi or grandmother.