I went on the Camp America programme several years ago as a horseriding activity leader. At the interview they just talk to you about yourself and the skills you identified in yourself on your application plus your experience of working with children and young people. if you opted on your application a preference for working at a camp for disadvantaged children they'll ask you questions related to that, or if you opted for a religious camp, questions related to that. I don't remember it being a scary or formal interview at all, everyone was very easygoing.
Specifically I was asked how I'd describe myself and how my friends would describe me, how I'd deal with a homesick child or one who seemed to have trouble making friends or joining in with activities, what I thought I'd find most difficult about camp and how I would resolve this difficulty if it occured.
Be yourself, be confident and have some questions of your own ready to ask the interviewers. The most important thing to the interviewers is that you come across as enthusiastic, competent and genuinely interested in the summer camp culture and atmosphere.