Representational State Transfer (REST) refers to a group of software architecture design constraints that bring about efficient, reliable, and scalable distributed systems. A system is called RESTful when it adheres to those constraints.
The basic idea of REST is that a resource, e.g. a document, is transferred with its state and relationships (hypertext) via well-defined, standardized operations and formats. Often APIs or services call themselves RESTful when they directly modify a type of document as opposed to triggering actions elsewhere.
Because HTTP, the standard protocol behind the Web, also transfers documents and hypertext links, simple HTTP APIs are sometimes colloquially referred to as RESTful APIs, RESTful services, or simply REST services, although they don't necessarily adhere to all REST constraints. Beginners can assume a REST API means an HTTP service that can be called using standard web libraries and tools.