When you despise things or people, you look down on them: you think they're really bad or really disgusting, so you hate them.
For example, if you despise roaches, that means you think they're gross, nasty, and awful. You absolutely hate it when you see a roach inside your home.
Something despicable is so terrible and so icky that people hate it: they despise it. These kids were expecting a clean pool to play in. Instead, they find a dirty, despicable mess of spiderwebs and live birds. And bird poop! There's nothing wrong with birds or spiders, but if you let them take over your pool and then expect kids to swim in it, that's despicable!