I have an old home with oak floors throughout. In high traffic areas the finish has been worn off and the wood is black. Is this dirt or water damage? Should I clean the wood before attempting to sand it down? If so, how?

Wood darkens with exposure to the moisture air. It also stains from dirt because it is porous. Damp mopping will cause staining when the finish is worn off.
You will need to sand below the surface to remove the stain. Use only a sand paper course enough to not get plugged up by the finish as it is sanded off. You could get by with only sanding the worn spots and matching the color of the surrounding floor, but this is very difficult to have it blend in.
Area rugs help to make these patches not so noticeable.

Great reply, thanks for the help!