A specific kind of mirror, the silvered-glass mirror, was invented by Justus von Liebig in 1835; but mirrors have existed since long before then. The first mirrors were pieces of polished stone or metal, and were made in 4000 BC. The first "modern-type" mirror, of glass with a metal back-coating, was invented in the 3rd century AD. And even back people had invented anything but spears and fire, you could still see your reflected image in a still pool of water.

So yeah, I would assume that the vast majority of people throughout history had at least some idea of what they looked like.