When there is chronic muscle tension or injury, there are usually adhesions which form bands of painful, rigid tissue in muscles, tendons and ligaments. These adhesions can block the circulation, particularly in the fascia and cause pain, inflammation and reduce movement.
Deep tissue massage works by physically breaking down these adhesions thus relieving the pain and restoring normal movement. To do this the therapist often uses myofascial release, direct deep pressure to the area or frictions applied across the grain of the muscles.
For most people yes there will be some pain, but this should be within your comfort and the therapist will be checking to ensure it is not too painful, otherwise your muscles will tense and restrict the improvement.
There is usually some localised pain after a deep tissue massage, but this should subside within a day or so. The therapist may recommend applying some ice to the area after the massage.