What does “hosting a web site mean”?
If you were hosting a party, it would probably mean that the party was being held at your house and you were providing everything needed to have a successful party: food, chairs, music, house, etc.
Hosting a web site is similar. The host provides the server, programming, and information needed for other people to view your site. So, when someone uses their browser (Internet Explorer, Firefox, Safari, etc) and types in a domain name, your website appears. Your host is also usually the person that manages and creates email addresses associated with your site and may make changes for you on your web site.
The server your web site lives on is typically a big computer and is very complex. It runs zillions of routines per web site daily, provides backups, processes forms, delivers emails, and many other tasks. Your web host is in charge of making sure things run smoothly, doing regular maintenance on the server to prevent problems, and handling problems if they do arise.