It's basically a large building full of servers. All sorts of things such as air conditioning, backup generators and powerful UPSs, as well as several links to the internet backbone, ensure your site stays online. The vast majority of sites are in datacentres, including this one. I actually buy webspace from a company that owns a server in the datacentre and "share" the server with others. However at the rate we're going, we might end up on our own server. There are even free places where you can host your site, such as
VP Host - Quality Free and Reseller Hosting.