If you want to pick up a coffee cup, your brain organically knows exactly how to bend your elbow and shoulder without doing conscious geometry. A robot must perform heavy real-time calculus to achieve this. This calculus is called Inverse Kinematics (IK).
The Mathematical Target
Forward kinematics involves knowing all the joint angles and calculating where the end of the finger will physically end up. Inverse kinematics operates backwards: the robot knows the exact XYZ spatial coordinate of the coffee cup in the room, and must work backwards mathematically through the lengths of its forearms and bicep to calculate what specific voltage angles to assign to each intermediate joint. Solving this equation at 30 frames per second allows for fluid motion.