It is an arrangement where you allow an agency to host your website for you on their Web Server for a fee.
The World Wide Web is a massive collection of web sites, all hosted on computers (called web servers) all over the world.
The web server (computer) where your web site's html files, graphics, etc. reside is known as the web host.
Web hosting clients simply upload their web sites to a shared (or dedicated) webserver, which the ISP maintains to ensure a constant, fast connection to the Internet.