In a nutshell, the web is a whole bunch on interconnected computers talking to each other. The computers (on the Internet) are typically connected by phone lines, digital satellite signals, cable and other types of data-transfer mechanisms. A 'data-transfer mechanism' is a nerd's way of saying: a way to move information from point 1 to point 2 to point 3 and so on.
The computers that make up the web can be connected all the time (24 hours in a day and 7days in a week), and they can be connected only periodically. The computers that are connected all the time are typically what is called a server. Servers are computers just like the one you use. The major difference; they have a special software installed called 'server' software.

Server software is created to 'serve' web pages and web sites. Basically the server computer has a bunch of web sites loaded on it and it just waits for people (web browsers) to request or ask for a particular page. When the browser requests a page the server sends it out.
The web surfer find a web site by typing in the URL, or in other words, the web site address. There are other ways to find web sites (like search engines) but behind the scenes web sites are all being found by going to the web sites official address. That brings us our last nerd detail; how does a web site get an official address so that the rest of the Web can find it!
Now to have your own web site you must
A) Register a domain name so that you can get a unique address to be available to the rest of the world.
B) Rent some server space.