You mean like flexing your elbow causes your hand to occupy a different place? (I'm trying not to use the word 'move'.)
Building the mechanical parts for a robot arm is more difficult than you expect. Servos were originally invented for the controls on model planes. Those controls are very light. The servo cannot lift the weight of the model.
So you need to find servos with enough torque that they can lift the weight of the arm and the servos on the arm. It should be obvious that the "finger" servos are smaller than the "shoulder" servos.