If you have a web site, you need to place the web site files on a computer somewhere in order for the world to see it. This computer, or server is called your ‘host’. So, your host server is just a computer stored in a secure place connected to the web.
It really doesn’t matter where your server is, as long as it’s up and running and connected to the web, and someone is maintaining it. Doing a search for “web hosting” or “web hosting reviews” will help you find both free and paid providers. Free hosting may include advertisements, but is fine for personal web pages. A complex site may require a more comprehensive package that provides database support or application development platforms.
Your host will also support the mail that goes with that domain. For instance, if your site is MyCompany.com, your e-mail address (you@MyCompany.com) will also be managed through that same host. Think of your domain as the street address and your host is the home at that address. When someone tries to find you or send mail to your address, they’re connected to your host.