Mirrors traditionally were pieces of glass backed with a coating of silver. Silver is a metal which has "magical" powers against vampires; something to do with the purity of the metal. Since mirrors were backed by silver, it would purify the image and not reflect the vampire.
This is also related to why vampires don't show up on film. Traditionally, silver nitrate or a silver halide is used to capture the image (and the image is also bounced off of a mirror anyways with SLR and TLR cameras).