Inverse Kinematics (IK) is a method of manipulating hierarchies where the Animator positions objects at the end of the hierarchy and the program calculates the positions and orientations of all the rest of the objects in the same branch.
With properly setup IK, you can quickly animate complex motions. For instance, the bones in the arm of a character are linked in a hierarchy, then limits are set for the rotations of the bones, then the animator can move the hand, and the IK will figure out what the rest of the arm needs to do.
IK is used in games to allow characters to interact with the environment in a more realistic manner, like when a character picks an object off the floor.
See also forward kinematics.