From what I understand, the Doppler Effect is the distortion that occurs when the source of a wave is moving relative to the observer, but more practically explained as 'that thing where a car drives past you and goes niaaow.' Now that I think of it, that's probably the only example I've ever heard given, and for a mostly good reason. There are a lot of things in the world that move fast and a lot of things that make a constant, loud, noise, but cars are some of the few things that do both and that most humans are familiar with.
However, the Doppler Effect becomes much more interesting upon the realization that it applies to all sorts of waves, not just sound. The Doppler Effect is understood in astronomy as redshift and blueshift; light from stars moving away from the Earth appears more red to us. and stars moving closer appear more blue.
Now that's all nice and sciencey, but I didn't realize until today that the Doppler Effect also applies to water waves. It's easiest to see in still water-- dropping an object into the water will cause a series of concentric circular ripples centered around said object. The Doppler Effect is that V-shaped ripple that would happen when you drag the object through the water. The object is still sending out circular waves, but since the origin of each wave is different from the last, a distorted shape is formed.