"Mirror mirror on the wall, who's the fairest of them--"
Have you ever wondered how mirrors are made? In order for a mirror to reflect properly, it's surface must be perfectly smooth. For the most part, a mirror reflects light; when light hits an object, some of the light is absorbed, some of it is reflected, and some passes through.
Basically, for a mirror to produce a clear image it has to reflect as much of the light as possible, and in order to do that it has to be smooth. A warped mirror scatters and diffuses light, making the image it produces look deformed. But a smooth mirror reflects without distortion. Which is what makes it possible for you to stand in front of the mirror and preen.
People have been admiring themselves in mirrors for a long time. Take the Greeks and Romans. They loved looking at themselves, although they only had highly polished pieces of bronze, tin, and silver.
Their descendants were even more vain; in 16th century, Venice mirror makers discovered the technique of backing a piece of glass with a reflecting metal composed of tin and mercury, producing a much clearer reflection. That technique is still in practice today, although now we use a thin layer of molten aluminum. Or sometimes we spray silver onto the back of a piece of glass in a vacuum to achieve premium smoothness.