Bone influence, or painted weights is similar to, but different from, IK. Think of IK in terms of a rope or chain, or for that matter, bones. IK allows you to grab the end of the rope, chain, string of bones, and have the rest of the geometry "follow" according to pre-determined physical constraints. For instance, right now in Anim8or, you can articulate bones individually, but you can't move one bone and have it "pull" on the joint of the adjoining bone(s). With IK, you can. For instance, you could move a model's hand and have the rest of the arm bones "follow" along.