An animation cycle is a set of images that are played after one another to create the illusion of walking or any other action/gesture.
An example is this image below,
Without these animations in Video Games. The games wouldn't be as immersive and not nearly as fun to play. Some of these animations can effect how the player interacts with there surrounding. For example, the jump animation. This allows the player to reach different heights and adds different mechanics to the game itself.