Deep tissue massage is directed specifically to individual muscle fibers. Its purpose is to unstick the fibers of a muscle while releasing deeply-held patterns of tension.
Deep tissue is a somewhat generic term, as there are many ways of doing deep massage. A common myth is that deep massage has to be painful. IT DOES NOT! Skilled deep tissue is about working with your body to reach deeper levels, not plowing through no matter what. Sometimes it can be uncomfortable or intense, depending on your body's condition, but a good massage should not cause you a lot of pain.