–Robert Louis Stephenson
According to Stuart Walton in Out of It: A Cultural History of Intoxication, children who spin around in circles until they become dizzy are an example of the universal human striving for altered mental states, or “intoxication.” Swinging on swingsets is another way to achieve Walton’s broadly-defined state of intoxication: if you arch your head back while swinging hard, you quickly lose sense of up and down, forward or backward. You are also liable to have a short “hangover” not long after you return to an upright position.
Another benefit of swinging is experiencing antigravity (really! at the peak of motion, when gravity and momentum cancel out) and walking in the sky (not really, but it looks like it for a fanciful moment).