REST is a fairly academic concept about how HTTP should be used for APIs. Although the properties that an API should possess so as to be considered RESTful are quite specific, in practice pretty much any API that is based on HTTP is now slapped with the RESTful label.
REST is any interface between systems that uses HTTP to obtain data or generate operations on that data in all possible formats, such as XML and JSON. It is a booming alternative to other standard data exchange protocols such as the Simple Object Access Protocol (SOAP), which has great capacity but also a lot of complexity. Sometimes a simpler data manipulation solution such as REST is preferable.