not wishing to sound too matrix like but the internet is everywhere.
Every computer attached to the internet including yours and mine make up the internet as a whole, any computer that is online has the ability to be a server, and in fact quite often is. For example in peer-to-peer networks (which are how most file sharing networks work) when you download a song your are not getting that song from a server in a big room somewhere you are downloading that song from another persons computer sitting in their back bedroom somewhere. and if you are sharing files then other users will be downloading those files from you.
The entire idea behind the internet is it is not owned by any one person/group/government, it is run for the good of the world and not for the good of one group of people. It is also designed not to be centralised so not to have a single point of failure (such as one large server room) if one part of the internet get blown up the rest of it will pretty much just carry on working.