If you are asking about RESTful APIs in general, that rather a larger question. To start with, an API is an Application Programmer Interface: basically, a set of hooks into a system, whether an operating system, an application, a webservice - anby large software system, more or less - that allows for programmatic manipulation of aspects of that system. The classic example of an API is an operating system's set of system calls, which allow the application programmer to access, in a controlled fashion, hardware and software managed by the OS.
REST (REpresentational State Transfer) is a particular means of communicating to a web-based service, using the standard HTTP GET, PUT, POST and DELETE operations. A given webservice that applies REST is called a RESTful service.
Thus, a RESTful API is an API that uses a RESTful protocol to communicate with the services it provides.