Can you dance the hula? Get into crazy yoga positions, or touch your toes? Then you're limber, meaning your body is pretty flexible and able to bend well.
Limber generally implies long and graceful limbs. Ballet dancers, it goes without saying, are limber. The term is also used for anything that's capable of being bent easily, such as a piece of metal or, in the metaphorical sense, someone's personality. More often, though, with this particular sense you'll find the word pliant used, implying easily manipulated. Good to be limber, less so to be pliant.