Good question. Space X makes money in two ways primarily.
(1) They launch multimillion dollar satellites into space for commercial clients and for government agencies
(2) They provide restocking of the ISS with their own shuttles, now that NASA no longer does that themselves
Regarding why space? The analogy to me is similar to when Europe decided to start sailing the oceans. Beyond just wonder, they did it for riches, new resources, new places to colonize and prosper. Eventually the western world became a safe haven for those who needed an asylum from political and religious persecution, and those who simply needed a fresh start.
The private sector can benefit by being the first to set up transportation methods, stations, communication satellites, and other ways to have access to the outer reaches of our planet. From there, entrepreneurs and government agencies will be compelled to explore what opportunities it has to offer.
Everything from mining, energy collection, waste disposal, research, and the like are fair game. And if you're the only guy to provide such access to outer space, there is a lot of $$$ in it for you.