To be mortified is to be extremely embarrassed. If your pants fell down in class, you'd be mortified.
In science, mortified describes body tissue that's severely decayed. But the most common meaning of this word has to do with hurt feelings, not rotting flesh. You're mortified when you're so ashamed or embarrassed that you wish you could just shrivel up and die — kind of like mortified flesh, actually. Though people get embarrassed often, being mortified is a little more rare and a lot more severe. It means about the same as humiliated.