To intensify is to increase the intensity, force, or power of something. For some people, Burning Man isn't intense enough on its own: they need to intensify it with drugs.
You can see the word "intense" in intensify, which clues you in to the meaning of the verb. When you make something more intense, you intensify it — make it more of whatever it is. Believe it or not, a pinch of salt can actually intensify the sweetness of the sugar in a cake. It makes it even sweeter. Storm chasers never know whether a tornado will continue to intensify or begin to abate as they approach — and the difference could mean life or death for them.