What is web hosting
In short
Web hosting is the server where your website lives and from which it is available to visitors. If the domain is the address, hosting is the house at that address.
Every site has to live somewhere. Hosting is the computer that stores your site's files and sends them to a visitor's browser when they open the site.
Hosting quality directly affects site speed. Cheap shared hosting is often slow because hundreds of sites share one server.
Why hosting matters
Hosting is the site's foundation. Slow hosting makes even a well-built site slow, and no optimisation fully fixes that. Decent hosting costs a little more but gives a solid base.