Fear of being in enclosed spaces. Not necessarily small spaces, although many claustrophobic people don't like these much either. The main issue is being trapped in somewhere you can't get out of easily. Claustrophobic people may avoid or feel uncomfortable in situations like flying in a plane, being in the middle of a crowd, or using an elevator.
Friend: Now we just take the elevator up to the ninety-seventh floor...oh, I forgot. You've got claustrophobia. Better take the stairs then *sigh*
Me: Actually, like many others with claustrophobia I still use elevators, because we don't let it control our entire lives.