Think of the internet as being a bit like the telephone system.
The "supercomputers" you talk about are a bit like large international telephone exchanges that route the data from one computer to another.
The actual internet web sites are not held on these "supercomputers" but as rojash says, it is stored on thousands, or maybe millions, of different computers.
If you pick up your phone, and dial a number in Australia, then the telephone system routes you to a phone in Australia.
Well with the internet, when you try to look at a site that exists on a computer in say Australia (an Australian government site for example) then the internet routes you the correct computer in Australia.
The internet runs on a technology called IP (or TCP/IP) and in fact each computer on the internet has its own "phone number" which is its IP address.
You may know Google in the uk as "www.google.co.uk" but the internet knows it as 66.102.9.104
In fact if you put the address below in the top area of your browser it displays the google uk page:
http://66.102.9.104/
In fact you can set up your own internet in your house with just 2 computers (it is called an intranet).
Connect them together, set a web server running on one of them (IIS comes with Windows), add some web pages to that PC, and the other PC could look at the web sites on the first PC.
The "real" internet works on the same principles (but more complex of course)