The ability to recognize a note without any other relative notes.
For example, if I hear a single note being played from a piano, I won't immediately be able to tell you which one it is. If you then play a few more notes, I would be able to work it out fairly quickly. Maybe you don't play anything else but I quietly hum a scale in my head and work it out. That's relative pitch and we can all develop this skill.
Someone with perfect pitch would be able to recognise the single note without any further help, from memory as it were. From what I've been told, you're either born with it or not. The fact that you can't really tell whether someone is actually just using relative pitch as opposed to perfect pitch shrouds the whole thing in controversy and many argue it's a myth, similar to a photographic memory.