15% of whatever money you pay doesn't go to a charity, it goes to them. This is not explicitly stated. See here: https://en.wikipedia.org/wiki/Humble_Bundle (search for 15%)
When you make a purchase on Humble Bundle, it by default has a divide between the developer or publisher, the charity being supported, and Humble Bundle. You can modify this percentage at purchase time, for instance, by sending 100% of your proceeds to charity, or stiffing the developers if you despise them.
Arguably, Humble Bundle bears a large chunk of the operating cost here, since they have to provide download bandwidth for things like the eBooks and non-Steam-based games. But only asks for 20% by default, from what I can tell. Of course, I'm sure Humble Bundle has done the math on how many people pay the default cuts, and how much they need to stay profitable as a business.
So, no, it's not that Humble Bundle is a charity, but yes, you can get games and books really cheap while supporting a charity.