Most of you reading this are only doing so thanks to the wonders of a modem or one of its descendants. What is this modem thing? Well the name is a geeky sort of hint: it stands for MODulator - DEModulator. This is not a great help to those of a less technical nature.
Well, computers talk in binary, which is 1s and 0s, which represent 'on' or 'off'. But your phone line - which is generally how people connect to the Internet - talks in analogue because it's an easier way of transmitting your voice. Analogue is a continuous wave, like you might see if you looked at a cross-section of the sea or if you wiggled a piece of string. So how can computers talk to each other if the phone line doesn't speak their language? Modems come to the rescue, that's how. They 'modulate' your computer's binary chatter into the clicks and burbles you hear when the volume is turned up on your modem. These strange noises are analogue and so can be passed down the phone line to the modem of a computer listening at the other end. This then 'demodulates' the noises back into binary for the receiving computer to understand. Modems also do clever things like error correction to make sure nothing got mixed up by noise on the line. Additionally they sometimes compress the messages so that they become smaller and can be sent faster.
These days all sorts of whizzy technologies are coming along like ADSL, DSL and so on... these, like ISDN, send the signals in a binary (aka digital) format all the way without modulating or demodulating. This is faster because there is less work to do and it's easier to compress and error check the data.