When your biceps brachii (upper arm) muscle contracts, ultimately and most directly, what is producing the movement?

It is the proteins present underneath the cells of the biceps brachii, which slide past each other lengthwise, thus shortening the muscle.  

The biceps crosses both the elbow and shoulder joints, its prime role is at the elbow where it flexes the forearm and supinates the forearm. The biceps brachii refers to a bi-articular muscle, that is, it assists in monitoring the movement of two different joints, the elbow, and the shoulder.