Someone who's tone-deaf has trouble telling the difference between musical notes. Being tone-deaf makes it hard to fully enjoy music.
While a person who hears the pitch of music in a normal way can distinguish between a higher and a slightly lower note, a tone-deaf person might not be able to hear any difference. Being tone-deaf can actually be medically diagnosed, although people who are tone-deaf can usually hear perfectly well otherwise. Since the condition is genetic, if you're tone-deaf you probably have a parent or grandparent who's also tone-deaf.