There are several versions of the answer to this question.

The most successful of them are not literally perceived (what he put on over one headgear of the other), but the type of wearing a hat. That is, “a hat wears ON a hat” will be synonymous with the phrase “a hat wears like a hat”. Another version suggests that "on the hat" is a hat with a certain curved crown. Another option: Bucket hat - the national headdress in some South American countries, their bucket hat in some way resembles a hat.