The mirror idea goes back to the idea that a reflection reveals a person’s soul, which is why many indigenous people believed that cameras would steal a person’s sole, also. So the idea is that vampires possess no souls for the mirror to reflect. Unlike the other apotropaics, mirrors do not actually ward vampires away. There is nothing preventing a vampire from standing in a hall of mirrors and attacking someone. Vampires avoid mirrors simply because they would stand revealed to the people.
Interestingly, though, mirrors present an oddity worth exploring. Mirrors function by reflecting light. One of the weaknesses of vampires is sunlight. Lastly, most mirrors were made by either polishing silver or silvering glass. Silver is a metal that also has a long-standing tradition for being regarded as pure because of its high shine.
While mirrors were also made out of highly polished bronze, the mirrors most people thought of, especially during the time that vampire mythology was at its highest, were the silvered glass mirrors.
What does this mean? Nothing, really. I find it an interesting conjunction of mythological ideas and beliefs.
Sidenote: Also, mirrors are essential for most camera photography. Many cameras include mirrors built into them, and film processes used silver compounds both for the recording of the photos and for the development of film. So, with the exception of modern CCD image sensors, vampires could also not be photographed.