A "network" is two or more computers hooked together. When two computers are "networked," information can be moved from one computer to the other. Companies have many computers on their network, so employees can share information with each other.
The "Internet" is an "international network of networks," or a whole bunch of computers all over the world, connected together.
Your Internet Supplier (sometimes called your Internet Service Provider, or ISP), keeps their computers turned on all the time, 24 hours a day, 7 days a week. They are a permanent part of the Internet. This way, whenever someone sends you an e-mail, it goes to their computer, where it is stored until you are ready for it. When you turn your computer on, and your computer connects to their computer, when you check your e-mail, the e-mail message goes the last part of its journey, to your computer.
Those "www.whatever.com" thingy's are called "Universal Resource Locators" or "URL's" for short.
When you use a "browser" program (like Microsoft Internet Explorer or Netscape), and you type in one of those "www.whatever.com" thingy's, your computer sends a request to the other computer, somewhere on the Internet (somewhere in the world). The other computer sends the "webpage" at that URL back to your computer, and you see it on your screen.
Every time your click on another link (which is actually another URL), it requests another "page" of information from that new URL. That new page may be located on the same computer, or it may be located on a computer on the other side of the world.
Because all these computers on the Internet are connected together, when information is being sent from one place to another, it gets passed from computer to computer, till it gets where it is going. If one computer is not working, the information is "automatically" sent by another route. This is what makes the Internet so robust. If some computers are not working, it doesn't block the communication. The communication is just re-routed automatically.
Note that this "information" being sent, could be an e-mail or a "www..." request for a page, or a page, or a file of information.