It broke because it is corroded into the caliper. While some have had luck in using heat and a screw extractor to back out the severed screw, I haven't and have had to buy a rebuilt caliper. My best advice is to buy a quality reversing screw extractor (Alden makes good ones; don't use the twisted hardened Sears versions). Treat it liberally with PBlaster, then heat the screw, cool it off with an ice cube and try to extract.

See also Gary DeFrancesco's trick of using an electrical welder to "burn off" corrosion in today's Brickboard digests: brilliant! He described it for exhaust studs, but I don't see why it would not work for non-ABS brakes.