The avatar defines an object’s skeletal structure but an Animator Controller is also required to apply animations to the skeleton. An Animator Controller asset is created within Unity and allows you to maintain a set of animations for a character and switch between them when certain game conditions occur. For example, you could switch from a walk animation to a jump whenever the spacebar is pressed. The controller manages the transitions between animations using a so-called State Machine, a kind of simple program written in a visual programming language within Unity. More information about state machines can be found here.
The avatar and animator controller are finally applied to an object by attaching an Animator component that references them. See the reference manual pages about the Animator component and Animator Controller for further details about their use.