A screw extractor is a very hard reverse-thread bit. You drill a hole into the screw, then carefully tap the proper extractor (which has a smaller initial diameter than the hole, and quickly flares out) into the hole, and use it to twist out what is left of the screw. The reverse flutes on the extractor cause it to bite harder into the metal of the screw as you put more force on it. Screw extractor bits are made of very hard metal, so they are very brittle. It is very easy to break one off inside the screw. When that happens you are screwed (sorry for the pun)- the extractor metal is harder than any drill bit, so you can't drill it out. The only recourse will be EDM (see below). To turn the extractor you should use a tap handle commonly used to turn threading taps. The screw extractor has a square end to fit into the tap handle. Using a regular wrench to turn the extractor is almost guaranteed to break it.