X/Y : X is for eXposition, or as they are more commonly called, Cat Shows.
The human went to a cat show in March and I wrote about it.
So I'll add some more links and photos here. You can find a cat show in your area by going to Cat Shows .US AB (All Breeds) rings refer to those where long-haired and short-haired cats are judged against each other; there are other rings where they are judged separately.
There are specific requirements for the judges when they look at the specific breeds of cats, such as appearance. With household pets, the important part is that they appear happy, healthy, clean, and well cared for. Sometimes the cats hiss at other cats; sometimes they purr when the judges handle them. Sorta like regular cats.
Some of the Maine Coon cats are reallly big. The one in the first picture is shown with a US dollar bill for scale.