API for site is a script (usually) that accepts requests (methods GET (site.ru/api.php?a=b), POST), and gives not a normal HTML for browsers, and the result of the query in a specific format (XML, JSON, php serialize()-ed).
Accordingly, it is intended not users and script with a third-party website/service/program that sends these GET/POST requests, gets the result and then uses the data. It sends queries naturally, and to perform a certain action (eg. as the actions performed by users of the site through the browser).
Users programmers need it for integrating with other sites/services, or automating some operations, creating an app for your website. Respectively need it is usually only very popular sites/services.