Perversion is a derogatory term for deviation from the original meaning or doctrine, literally 'turning aside' from what is perceived to be orthodox or normal. A pervert is a person in a state of perversion. By apocopation, a "pervert" becomes a "perv"; what he or she does is "pervery". It often refers to "sexual perversion", more neutrally and medically called a paraphilia.
The verb form of the term, in conventional use, simply means to turn something away from its natural state (or what is perceived to be its natural state.) For example, one might say that the modern film version of "Romeo & Juliet" perverted the story.
Within the BDSM community the term pervert has few if any negative connotations. It is often used ironically in repossession of the term by its objects. So, a BDSM participant might greet another by saying, 'How ya doing, you perv, you?!" Fetish clubs may advertise themselves with a phrase like "a night of pervery".