If something's tattered, it's worn ragged. You'll understand tattered if your dress has been dragging under your car for the last 100 miles. It will be a tattered mess.
Tattered often applies to clothes. If you're a nice guy, you might give your coat to the homeless man with the coat that's so tattered it's threadbare and see-through. You can also use tattered figuratively, for something that's in shambles, like the tattered reputation you would have if you embezzled from your grandmother. The word tattered comes from Middle English, from a time when people wore clothing with decorative slashes, and apparently tatter originally meant "a scrap of cloth."