Our muscles give us the ability to move our arms but....?
I am a bit confused as to what you are asking. You don't move your arm, like your suggesting, ever. No one does, and no one can. You contract your muscles which happen to move your arm. The movement of the arm is the result of your muscles contracting, not the cause.

How it happens is that your brain sends a signal to your muscles (which you cant feel). The muscles get excited and they contract. The instant your muscle contracts your hand begins to move. In the end your bones are like sticks, and your muscles are the ones that pull the stick in different directions, in order to achieve flexion and extension.

Might i suggest you read up on the musculoskeletal system (http://kidshealth.org/teen/your_body/body_basics/bones_muscles_joints.html) ?