The muscles that lay just underneath the breast are commonly known as the 'pecs' or pec major and are one of the strongest groups in the upper body. There are actually two muscles that make up your pecs, the pectoralis major and the pectoralis minor.
The sternal head of the pectoralis major is a lot stronger and is responsible for much of the shoulder flexion movement when the arm is being internally rotated. To envision what this movement would look like, imagine if you were to stand with arms at your side and then lift them both upwards until they reach shoulder height and then inwards so that they move on an angular path. This would be the pectoralis major muscle making the majority of that movement.
The other main movements that this part of the pec is responsible for when it comes to shoulder movement are transverse adduction (moving arms inwards while they are behind you), internal rotation, simple adduction (bringing arms to the sides of the body) and extension (bringing them back). Keep in mind that other muscles will also be working in these movements as well, but the pectoralis major will be acting synergistically.
In terms of muscle appearance, the pectoralis major is large and fan shaped and covers the upper portion of the chest. Usually when well developed on males you will also get a nice dividing line between either side of the muscle (line running along the sternum).
The pectoralis minor on the other hand is a thin and flat muscle that lies beneath the pectoralis major. It is considerably smaller and is usually much weaker in terms of strength. Its main role in movement is to draw the scapula forward and downward when the ribs are fixed into position.
As already stated, since this is likely the largest upper body muscle on your front side, it is critical that you target it during your workouts. As a nice added benefit, most exercises that work the chest will also work the triceps as well so you will be able to reduce the amount of time you dedicate to those muscles.