What is it exactly ?

Massage:  The application of soft-tissue manipulation techniques to the body, generally intended to reduce stress and fatigue while improving cirulation.  
Bodywork:  Various forms of touch therapies that may use manipulation, movement, and/or repatterning to affect structural changes to the body.
Somatic:  Meaning "of the body."  Many times this term is used to denote a body/mind or whole-body approach as distinguished from a physiology-only or environmental perspective.

Will my insurance cover it ?

The services of a bodywork professional may be covered by health insurance when prescribed by a chiropractor or a osteopath.  Therapies provided as part of a prescribed treatment by a physcian or registered physical therapist are often covered.