From LightWiki

A method of solving the angles of the joints in a chain or limb, so that they reach, or come as close as possible to, a specific point. This is different from forward kinematics where each of the joint angles is specified and the end of the chain ends up wherever it ends up. Ik simply moves a goal object, and the limb adjusts itself without user intervention.

IK would typically be used to make a character reach for a specific item, for walk cycles to avoid the feet slipping on the ground etc.

( need more from someone who knows!!!! - james )