Does anyone know how rock climbing shoes work? Like what makes them be able to stick to rocks so good? I heard it was because of type of rubber they use is different then normal? But I'm not really sure if that's it?

Yes they do work. You are correct that the rubber is "sticky" but it's also because of the way the rubber is positioned: from the sole it extends around the sides, which gives more grip. It's a nice combination of "feel", protection, and performance.

Just bought my first pair of rock climbing shoes and love them! They need to be a snug fit.