Why do people organize summer schools?
A summer school is usually a way to have a focused series of lectures on a specific topic. The best analogy I can think of is that of a master class for musicians. The audience are students who are usually sufficiently adept that they can handle the intensity and focus of a short program taught at a high level. For example, if you're just starting out in grad school in computer science, a summer school in specialized aspects of (say) deep learning might not be very useful. This at least partially answers your first question.

Summer schools are useful because they can bring a set of experts on a topic together in one location, at a venue where this expertise might not otherwise exist. In computer science, this might also be part of the explanation of why there are so many summer schools in Europe: since many topics in the field are dominated by the US, it makes sense to have summer schools in Europe for the reason above. 

The speakers of course get the opportunity to travel and teach a focused group. It's a prestigious thing to be invited to such an event. The organizers make their mark (and benefit their institution) by organizing such an event. The students learn about a topic that they might not otherwise get exposure to, from the experts in the field. And that is an answer to your second question.