Simple Object Access Protocol (SOAP) relies exclusively on XML to provide messaging services. An interesting SOAP feature is that you don’t necessarily have to use it with the Hyper Text Transfer Protocol (HTTP) transport.
Representational State Transfer(REST) provides a lighter weight alternative. Instead of using XML to make a request, REST relies on a simple URL in many cases. In some situations you must provide additional information in special ways, but most Web services using REST rely exclusively on obtaining the needed information using the URL approach. REST can use four different HTTP 1.1 verbs (GET, POST, PUT, and DELETE) to perform tasks.
To describe both in a single word, these 2 Protocols are used to access web services.
Another answer, from Debasish Chakrabarty on the Content Development Team:
Web services allow a client application to request data and computations to a web server and the web server to return responses. The client application could be a web browser or a web service application. Web services commonly enable client applications to communicate with web servers through the use of standard web protocols, commonly HTTP.
The web services are primarily based on:
• Simple Object Access Protocol (SOAP)
• Representational State Transfer (REST)
Simple Object Access Protocol (SOAP) is a protocol for exchanging structured information between applications (client and server). It provides a messaging framework that allows applications to pass messages back and forth in the implementation of web services over a network. SOAP uses Extensible Markup Language (XML) for formatting messages that are commonly transferred using HTTP.
Representational State Transfer (REST) is a client-server software architectural style for distributed hypermedia systems, such as hypertext, audio, video, and image. The architectural principles defined in REST are used for developing web services. A web service based on REST is called a RESTful web service. REST makes use of existing web protocols commonly HTTP.