There is a very interesting feature of the human eye actually allows animation to exist. It is in fact a flaw in our eyes that is known as persistence of vision; first written about by Peter Roget in his paper The Persistence of Vision with Regard to Moving Objects.
When an object is placed in our line of sight and then rapidly taken away, we actually see the object there for a fraction of a second longer then it is really there. If that first object were taken away and then replaced by a second object, the persistence of vision would actually blend the two images together to make a smooth transition.
Imagine if we didn't have that flaw in our eye and we did in fact see every movement of an animation. When the first cel were taken away and quickly replaced with the next we would see a moment where there was no picture at all [the moment when the pictures were being switched]. This would give all animation a very jerky look to them, and it wouldn't look like the characters on screen were moving naturally at all.
To better illustrate the idea behind persistence of vision take a look at the two animated images below.