How do I repair terrazzo floors?
It's possible, but probably something that you would call in a professional for.  Even assuming that you had epoxy resin based floors, you'd still have to match the existing colors and sizes of the terrazzo pieces, clean out the nail holes, refill them, and grind and polish so they're level with the rest of the floor.

EDIT: Found this article that suggests that repairing an epoxy based floor might be easier than I thought.  I'd still get some professional advice first though.