Someone who acts out of the accepted norms, usually in relation to sexual activity. One who has enjoyment or satisfaction in doing what the majority consider to be abnormal, or not socially approved of.
Usually used in reference to sexual behaviour, however can refer to the way one adapts something common, such as their production of a classic play, in which they are said to have "perverted" the original concept.
Homosexuals were considered 'perverts' until recently, though in some circles, homosexuality is still thought of, as being a 'perversion'.
In other contexts, the Catholic Church would refer to someone who was Catholic, that left the fold to become Protestant, as a Pervert. It is still used today, in that context, by some of the more extreme Catholic Orders.