When a web designer builds a web site, he is creating a set of files or documents. These are much like the files you create with your word processor.
The web files need to be linked to the rest of the Internet so people can browse them.
A web hosting service (also known as a Web Presence Provider or WPP) runs special computers that are linked to the Internet. These computers are "web servers" and they "host" web sites.
By paying monthly rent, you can place your web pages on a web server. Once your pages are on the web server, they are visible to the entire Internet. This is "hosting" your website.