Okay, so we have two computers, joined by a piece of wire, that can transfer information between them. What happens when those computers are in different cities (or even countries)? We don’t have enough wire!
We don’t have enough wire, but rather conveniently the telephone companies do, so we use theirs.
To make a telephone call, we dial a number and wait for someone to answer. All we have to do is get the computer to do the same thing.
If you listen to your telephone when you dial a number, it usually plays a different note for each number (this is called “tone dialling”, there is another, older system called “pulse dialling” that doesn’t do this, but for the sake of simplicity we will ignore that), so if we get our computer to make the appropriate beeping noises down the phone line it will be able to dial telephone numbers.
After the call is answered, we need to send our information. Now, our computer wants to send electrical pulses, but the telephone expects sounds, so we need something to convert (modulate) those pulses into sounds and back again (de-modulate). Every time our computer wants to send a binary one it needs to go “beep” and every time it wants to send a binary zero it needs to go “boop”.
There we go, we’ve just invented the modem (MODulate DEModulate) and can now transmit and receive information to and from any computer by connecting it to a telephone line.