Analog vs Digital

In electronics the terms analog and digital come up a lot.

So what's the difference?
Analog means that a value is represented along a continues scale.
Digital means that values are represented in only one of two states (on or off, 1 or 0, true or false, etc).

If you think of a push button, it is either on or off, so it's a digital input device.
It either sends a pulse, or not.

A potentiometer, on the other hand, can be moved to a wide variety of position, so it creates a variable resistance, which we can read into the Arduino board as an analog value

This video takes you through the basics of analog and digital signals (don't think of this video as old, think of it as RETRO!):

This video relates the ideas of analog and digital signals to the Arduino:

The following websites are also good sources for learning a bit more about the differences between analog and digital.
This chart compares the two, analog and digital.