Your vertebrae have nerves running through it which extend to the arms and legs. The nerve that has been pinched passes through the foramen which is an opening at either end of your vertebrae in the neck.
 

A pinched nerve interferes with the conduction of the nerves, which is how the brain and sensory signals get transferred throughout the body. When this happens, the nerve gets exposed or interrupted, which breaks the conduction.
Because of the pinch; fluid tends to gather around the damaged area resulting in inflammation which further increases discomfort and pain. This pain is very disabling, as it makes even simple neck movements extremely excruciating to perform (the most common pattern of pinched nerves usually occurs on one side which makes the rotation difficult and painful to the same side).
Massage therapists are trained to perform treatment that can reduce pain and gradually help the patient gain back range of motion in the neck.

They will show you a few stretching as well as some basic neck exercises that will help ease the pain to an extent. Depending on the diagnosis, a massage therapist will decide what type of hydrotherapy (hot or cold) would be suitable for the condition.

Usually, initial discomfort will be noted for a couple of days post treatment, but the client will slowly regain their range of motion and pain will dissipate.