This is a quick way of creating a namespace for constants.
You can of course achieve similar effect using a struct, however running let foo = StructOnlyForStoringConstants() will not throw an error or even a warning (can be solved using private init or even logging a warning, but we quickly lose the quick in a quick way above) and hence might be confusing (some argue). Since enums without cases (or "no-case enums") cannot be instantiated, you don't have this problem.
Another reason is that putting constants in an enum might feel more natural (than say in structs), as enums are used for storing a group of related values.