I think the phrase you want is 'Web Services'. Look there for a lot of info.
Basically this is an API that is designed to be secure, maintained and stable over releases. This takes a lot of time to get right so they are expanding slowly.
Other people are knocking together quick web services (installed as a 3rd party plugin) but it's very likely that they will break in future or, worse, open up security issues on your server. Check such code very carefully before relying on it.