From Rap Dictionary
- Jigga is a shortened form of the old racial epithet 'jiggaboo' commonly applied to African-Americans well into the 1970's.
- Jigga is one of the many nicknames for Jay-Z, put Nigga and Jay-Z together and you get Jigga. "Y'all can never diss Jigga, get nothin for that" -- Jay-Z featuring Kid Capri (It's Like That) 
- A less inflammatory alternate for the word nigga.