xkcd mentions the mirror writing puzzle in the hover text for today's comic. That this is a puzzle has always puzzled me.

The text in a mirror is backwards because you've rotated the book 180 degrees in order to present the text to the mirror. It's backwards because you've turned it backwards.

And, there's no mirror needed to demonstrate what's going on. Take a single piece of paper, write "HI" in big black letters and hold it up to a light so that the text is facing the light (as if the light was a mirror). In other words, show the text to the light. Given a bright enough light and thin enough paper, you'll see through the paper and you'll see that the "Hi" is reversed.

It's not vertically flipped because you didn't flip the paper vertically when you held it to the light.