Welcome to the Ripple Documentation. This uses a slightly more advanced system than the one on the website, and is used mainly for documents for those digging really deep into Ripple, or just developers who want to look at the API docs. The Ripple API allows developers to interact with Ripple itself, being able to fetch data like an user's stats and all sorts of cool stuff. Basically, it allows cool people to do cool things.
If you're interested in interacting with the game directly, by for instance checking an user is online, you should check out the Bancho API. If, instead, you're interested in fetching information about an user, you should go see the API. If you're interested making your application (which relies on the osu! API) compatible with Ripple, you should check out the documentation on the peppy API (a subsection of the API).