Why do humans masturbate?
One word. DOPAMINE 

See this article on Reward System and this one on Dopamine Those basically answer your question as to addiction, urge, and feelings of relaxation.

There is absolutely nothing wrong with masturbation, so long as you realize that it is a healthy expression of one's sexuality, that is observed, quite frequently, in our nearest relative, the Bonobo. There is no shortage of the study of primate masturbatory practices in the literature, and one could make a career out of its scientific study and analysis, so if you are interested in learning more, conducting a Google Scholar search on Primate Masturbation should give you literally years worth of reading material.

As for an actual addiction, it would only develop into a pathology if it became disruptive to one's life and was pursued at the exclusion of other basic activities.