osu! has a public API that third-party services can use to expand and support the osu! platform. It used to be more private, only to be used on a per-request basis, but now anybody can use the API so long as they have an osu! account.
You can find documentation of the API at osu-api's Wiki. The current version of the API uses private keys to authenticate requests. You can apply for an API key at the application page on osu!'s website. Note that the documentation on the osu!api wiki may not be entirely complete or extensive, and the API itself is not under active development.