It's okay to leave your wild mass guesses here, if you don't want them anymore.
Exactly what it says. Malachi's mother wanted a prestigious child, and instead of conceiving the typical way, chose to use a sample from a "genius" donor in the hopes of getting one who would be genetically exceptional. She dumped him at the camp once she decided Malachi was a failed experiment. Malachi remembers only that his dad was a genius, either because his false memories protect him from the realization or because his mother compared him to his father without elaborating on what that means, he just assumes he has a father because it's the logical thing to think.
No counselors, no staff of any kind, but full of still-standing cabins and structures, able to provide uniform shirts for campers somehow? This clearly was a real summer camp at some point. The people that built and/or ran it eventually had to abandon it, turning it into a place forabandoned things.
Some kind of supernatural force calls out to people who have unwanted things, and compels them to deposit those things at the camp. Everything at the camp, from the kids to the food to the books in the library, right down to the cats dropped off by parachute, are all unwanted, and were collected by the supernatural force that is the camp. The supernatural force may or may not be malevolent, as it clearly provides for its residents, but it also leaves them alone most of the time. The only way to escape the camp is to become self-actualized: you have to learn to want and value yourself, at which point the camp releases its hold on you.