Symbolism, Imagery, Allegory
Since mirrors reflect images back, they're often used in books and movies and art as symbols for truth. For a prime example, think of the mirror in Disney's Snow White movie—it's always blowing up Snow White's spot. So it's fitting that the mirror is how Bobby first realizes he's no longer visible in Things Not Seen. Check out this discovery that his reflection no longer exists:
It's after the shower. That's when it happens.
It's when I turn on the bathroom light and wipe the fog off the mirror to comb my hair. It's what I see in the mirror. It's what I don't see. (1.2-3)
Now that his reflection is no longer present, does that mean that Bobby doesn't exist? Of course not… but it does mean that he has to find new ways to define himself. He can no longer define himself by whatever he sees in the mirror. Without the crutch of a visible appearance, Bobby starts to look inward in order to figure out who he is, and who he wants to become.
In the end, Bobby doesn't even stop to look at his mirror as he rushes out the door to tell Alicia that he loves her. He doesn't need something else to tell him who he is or what he should do—he already knows that:
As I open the front door, something moves. I turn, startled. It's me, in the big hall mirror. But I don't stop to look. I'm out the door. I'm in a hurry. I've got to get over to Alicia's house. I need to tell her how much I love… how much I love her poem. (28.97)
Instead of letting the mirror tell him who he is, Bobby just goes and does what is right for him—and that's going to tell Alicia that he loves her. He sees himself clearly now, and it has nothing to do with how he looks.