Deep Tissue means vertical pressure downward into the muscles. Leveraging her body weight, the massage therapist applies precise pressure and waits for her hand or arm to move, which signals that the muscle has released.
Within Deep Tissue there are a number of techniques, the most common of which is probably cross fiber friction. Cross fiber work involves applying the stroke in the opposite direction of the muscle fibers with slight movement back and forth to break up tension.
With Deep Tissue, if you cannot breathe into the pressure and relax around it, then the amount of pressure needs to be adjusted. The sensation should feel more like “hurts so good” than “holy crap when will this torture be over.”