Toggles inverse kinematics on and off.
When IK mode is off, forward kinematics is in effect. In this mode, child objects inherit the transformations of their parents, so when you transform a parent object, you transform its children as well. If you transform a child object, the parent is not affected.
When IK mode is on, inverse kinematics is used for position and rotation transforms. As a result, when you move or rotate a child object, its parents follow, on up through the chain of the hierarchy.