What does it mean when you a say programming model is RESTFUL

Representational state transfer (REST) is an abstraction of the architecture of the World Wide Web; more precisely, REST is an architectural style consisting of a coordinated set of architectural constraints applied to components, connectors, and data elements, within a distributed hypermedia system. REST ignores the details of component implementation and protocol syntax in order to focus on the roles of components, the constraints upon their interaction with other components, and their interpretation of significant data elements.

Representational State Transfer (REST) is a pattern that allows you to represent http requests to a server via URL's  and content that are created in  a specific way.   The slash separated words of the URL are the resources of the call.  The Methods of the request (GET, PUT, POST, DELETE represent the operations of the call).  Often the methods are one-to-one mappings with CRUD (Create, Read, Update, Delete) operations on the server.