I'd split the explanation into two parts - hull and systems. Hull damage can be patched to hold air, but armor points could only be repaired using actual armor replacement parts (so either an engineering ship or a yard). Ship systems can be jury-rigged, but some sort of point-system should be employed (maybe tonnage, or some hull percentage for points?) using onboard spares. By default a ship carries X points in spares, a workshop gives you X+Y points in spares. You could carry more points as cargo if you wanted to (important for ships not planning on heading back to civilization any time soon).
I'd also put some verbiage in there about salvaging parts/points from other ships. There's really not much out there on how that would normally work, and you had a tussle with a pirate (or are pirating yourself) it'd be nice to know what you might expect to get off the other guy to patch your own ship up.