How do mirrors actually work?

Why do mirrors flip faces horizontally but not vertically? James May explains, with the help of a very childish prank.

A mirror is made from a sheet of glass with reflective material applied to one side. It is like an old fashioned transparency photograph viewed the wrong way around. It doesn't reverse left and right, it reverses back to front. As James May explains this is nothing to do with the mirror itself, the writing appears back to front in a mirror because we present it back to front.