Something that's perverse is deviant — it's not completely acceptable, and it may be even a little strange. Your perverse sense of humor probably makes some of your friends laugh while others just look uncomfortable.
Something perverse is unusual, possibly somewhat weird, and even immoral, like that time the odd kid in class announced that a love poem was really all about lovingly poisoning squirrels and no one sat next to him for a week afterwards. That kid's perspective was perverse. Perverse can also mean "stubbornly contradictory" or "perverted." The word originally meant "wicked," from the Latin perversus, "turned away or askew," and figuratively, "turned away from what is right."