Ukemi is the art of falling. In aikido, this involves learning to take yourself from a state of balance through a state of unbalance right back to a state of balance. This usually involves rolls, but there is also a more dramatic form of ukemi called a breakfall which is used in drastic cases (a very powerful throw, or the chance of breaking oneself into tiny pieces). In aikido, ukemi generally flows very nicely and is also useful in daily life at times. (hey, it's saved myself from getting hurt a time or two...)

I'd have to add that ukemi to me seems more than just taking falls. It seems more a method of allowing yourself to be led without injury; taking falls can sometimes act as a part of that.

Ukemi requires relaxation and an awareness of your partner's actions and motivations. Sometimes taking ukemi doesn't involve falling at all, but instead just requires you to shift your weight or pivot on one foot or whatever the situation calls for.