Animation is the process of giving your model railroad artificial life through movement or sounds beyond the train itself. Examples include moving people, lights that go on/off, background sounds, moving equipment or vehicles, etc. Animation can be very simple or quite elaborate involving a series of related movements. For example, there are indoor layouts where a simulated fire gets triggered in a house and minutes later a firetruck arrives and the fire then disipates.
Animation has existed on model railroads for many many years, but it is a little easier with DCC. There are components that allow for detection of events such as a passing train. These same components can then send electrical signals which can be used directly by your animation device to trigger some movement, sound or light effect. With DCC it is also easier to trigger multiple effects using the same trigger event.