SOAP is a protocol for exchanging XML-based messages over computer networks, normally using HTTP/HTTPS. SOAP forms the foundation layer of the web services protocol stack providing a basic messaging framework upon which abstract layers can be built.
As a layman's example of how SOAP procedures can be used, a correctly formatted call could be sent to a Web Service enabled web site - for example, a house price database - with the data ranges needed for a search. The site could then return a formatted XML document with all the required results and associated data (prices, location, features, etc). These could then be integrated directly into a third-party site.