A mirror reflects an image, a lens flips an image. Yep, the image that hits the back of your eyeball is inverted up/down and left/right. Which is perhaps why if you work with a large format (ie. no viewing system 4X5 or 8X10 camera) camera long enough (and it takes day in and day out use to get to this point), the upside down and reversed image doesn't look "odd" to you anymore, you're able to convert the image mentally back into a right side up, right reading image.
The best way to get your mind around what happens with a mirror is to use tracing paper, as someone mentioned above. The mirror is merely reflecting back an image of what another person would see, were they in exactly the same spot as your eyes are in the mirror.