RESTful API's use a specific URL format and a set of HTTP request headers in order to indicate if the request is a Create, Read, Update, or Delete request (a.k.a. CRUD). Rather than trying to explain it all here, I suspect a simple web search on "restful API" will tell you everything you need, probably better than I would off the top of my head. 😉
PS: While a database is normally involved, that's not required for an API to be RESTful -- just that it follows the relevant URL formats and use of HTTP headers.