In short REST is stateless architecture that runs over HTTP and is often used in mobile applications, social networking Web sites etc etc.
REST involves reading a designated Web page that contains an XML file. The XML file describes and includes the desired content. The REST style emphasizes that interactions between clients and services is enhanced by having a limited number of operations (verbs).
REST has been applied to describe desired web architecture, to identify existing problems, to compare alternative solutions and to ensure that protocol extensions would not violate the core constraints that make the web successful. Fielding used REST to design HTTP 1.1 and Uniform Resource Identifiers (URI). The REST architectural style is also applied to the development of web services as an alternative to other distributed-computing specifications such as SOAP.