I have a floor drain in my basement that is backed up. It has a "ball" in it- what is that for? There is a plug in the side that I assume goes strait into the main line. How do I clean out the drain?

I have not seen a floor drain that comes with a ball. Try taking the ball out.

Does it look even remotely like this? Flood guards for floor drains - check valve to prevent flooding from FAMOUS PLUMBING SUPPLY You could have a check valve in your drain to stop possible flooding. Any chance of a picture?

The ball sounds like what Bal said. A backflow preventer. The plug is a floor drain clean out and it bypasses the trap to give you a clear shot at snaking the drain line. Good luck, Tom