Writing an API can be as easy as taking the results of some database query and presenting it to the user. A more advanced one can often present the data in one of multiple formats. The user can then specify which format they want.
JSON is currently the most popular format for new APIs. XML is another common one and was certainly king before JSON hit the scene. An API might choose to make an HTML format of the data available, whether in some representation of the data or to render documentation about the API itself. Of course there are many others.
Mojolicious believes in Content Negotiation, as it is called, and supports it throughout the stack. Mojolicious makes it easy and convenient for users to pick a format they would like. Similarly it makes rendering the different formats easy on the site author, as you would expect.