The pectoral girdle.

A bird has 175 or so muscles to move it around in an almost infinite number of ways - flying, walking, diving, feeding, preening, courtship, etc. That's far too many for us to discuss here so we'll limit ourselves to the most important function, flight, and we'll limit ourselves further by only discussing the flight muscles that provide the power for flight: the pectoralis and supracouracoideus. These two muscles alone account for 15-20% of a bird's total weight.

As the diagram shows, the largest muscle, the one you first cut into when carving a turkey breast on Thanksgiving, is the paired pectorals muscle. One end of the muscle attaches ventral part of the keel of the sternum and the other to the medial end of the sternum. When the pectoralis muscle contracts, it pulls the wings down on a power stroke. 

The other muscle, the supracoracoideus, is attached to the dorsal part of the keel of the sternum, closer to the body. When you cut into the turkey breast, you slice into the supacoracoideus second.  This end of the muscle attaches to the other side and above the medial end of the humerus. When this muscle contracts, it pulls the wing up in a recovery stroke.

 So, the pectoralis pulls the wing down and the supracoracoideus pulls the wings up. This opposing structure of the two muscles of the sternum works because of a pulley system. The supracoracoideus passes through an opening called the foramen triosseum, or hole between three bones: the humerus, coracoid, and scapula (see avian skeleton).

Now, in flight, the wings don't just move up and down; the bird would go nowhere. A series of other muscles twist the wing, adjust the wing feathers, and move the tail in order for the bird to fly  or soar in a particular direction. You can read about flight on another page and look at this video.