The Internet
Hosting is when the files for a website or online service are stored on a server that is online, so other people can reach the site. If you hosted a site on your own computer at home, it would only be reachable while that computer was switched on and connected, and it could be slow for visitors far away.
Most websites and online services are hosted by a hosting company. The company runs servers and keeps them connected to the Internet all the time. You upload your website files to the company's server, and visitors' browsers request the pages from there.
The hosting company stores the files, but you still need a domain name that points at the hosted server. That is the name visitors type or click, and it must be set up so that it leads to the server holding your site.
For example, a school chess club could pay a hosting company to store its fixtures and results pages. The club does not keep a server in a cupboard; the hosting company's server stays online, and the club's domain name points visitors to it.