Off-center things aren't in the exact middle. The part in your hair may be off-center, and so may be your political leanings.
The meaning of off-center is fairly obvious: not right in the center, but off to one side. It's frustrating to watch a movie that's projected off-center, and if you're very particular, it might drive you crazy to see a knocker that's off-center on your friend's front door. This adjective also means "a little weird" or "eccentric." An off-center sense of humor is wacky and strange, and if you're feeling off-center, you might be coming down with the flu.