A web Host is simply a pc where many websites (sometimes thousands of websites) are hosted, and of course, the web host service is provided by a web hosting company.
This web host is nothing else that a fast pc like the one you have at home; however, if you are like most people, every night you turn off your pc. So, imagine if you turned of the web host every night: nobody would have access to those websites hosted in that pc until you wake up the next morning, and remember to start up your pc again.
Also, web hosts are connected to the internet at real fast speeds, and not the regular speed that you get at home with your ADSL connection.
Besides speed, there is the issue of security. Most large web host companies have completely secured servers against hackers, data loss, and power outage. Having these types of security characteristics configured for your personal web server could cost you thousands of dollars monthly.
Also, the need of 24/7 support makes it very difficult for small one person companies to run a good web server.
So, there you have it, a web host is simply a powerful PC, called a server, where many websites are installed, and is routinely being monitored against hacks, fire, data loss by specially trained support people.