When the specified muscle shortens, it pulls on the corresponding bone at its insertion point. The contraction shortens the distance of the angle between the articulating bones, with the joint acting as the fulcrum. Upon receiving the signal to relax, the muscle opposing the contracted muscle will then act to extend the movable bone back to it original position.
The skeletal system provides structure for the muscular system to move. For example, if you hold your arm straight and bend the elbow, you will your bicep move up your arm.
Without the skeletal system the body would be like a blob on the