From Wikipedia, 2010 March 15th

A web hosting service is a type of Internet hosting service that allows individuals and organizations to make their own website accessible via the World Wide Web. Web hosts are companies that provide space on a server they own or lease for use by their clients as well as providing Internet connectivity, typically in a data center. Web hosts can also provide data center space and connectivity to the Internet for servers they do not own to be located in their data center, called colocation.

Not too complicated, but not that simple to understand too isn't it? Here's my version of what a hosting is:

Web hosting is a service which offers a place somewhere to store web pages and emails, as well as make them accessible via Internet.