In many places in the US, there are public swimming pools. During most of the day, the pools are open to all ages. However, some pools set aside certain hours for adults to come in and swim laps for exercise. During those hours, the adults don't have to worry about toddlers screaming, or kids playing with toys and taking up room, or teenagers playing games and flirting. It is just adults, swimming laps. That will usually be on the pools' schedules as "Adult Swim." No children; only adults should participate. Cartoon Network making a comparison to the pools' schedules. They're saying that the shows are only for adults, not children.

Hey! Many public pools in America have a few hours every day where children are not allowed. This is usually called "Adult swim". Pools and cartoons are both usually play things for kids but for a few hours each day adults can enjoy them. Also your English is perfect. :)