Animator Component: It may differ to what you plan on animating.

For Example a 3D humanoid character will have a different animation than a 2D Character.

Animator controller
The Picture with a model attached, With the model there is an animator controller present. The first component in the Animator controller stores a reference to an Animator Controller asset.
Animator Controllers are used to determine which animation is being played in the scene.
For example you can tell you animator controller to program your model, to when it is suppose to be standing running or jumping. It will then play and blend the animation automatically


Avatar
An avatar is the asset that unity creates when importing a 3d humanoid.It contains a definition of the skeletal rig that the model has. Try to think as the avatar is the glue thats joins the model to the animation that binds it to the animator.
NOTE: For models with no skeletal rigging, an avatar is not required.

Apply Root Motion
The Root Transform is a projection on the Y plane of the Body Transform and is computed at runtime. At every frame, a change in the Root Transform is computed. This change in transform is then applied to the Game Object to make it move.

The Animation can be looped using the Root Transform or Using the Script that can be applied to the avatar.

This script is created with a function, (underline in red) and then it is attached to your game object.

Animate Physics

When turned on, animations will be executed in the physics loop. This is only useful in conjunction with kinematic rigid bodies.

An animated platform can apply velocity and friction to rigid bodies sitting on top of it. In order to use this, animate Physics must be enabled and animated object must be a kinematic rigid body.

IMPORTANT : AVATAR MUST HAVE A RIGID BODY

Culling Type

When culling is enabled, Unity might stop animating if it thinks that the results of the animation won't be visible to the user. This could save you some performance if you have things animating outside of the view port, whose animation is only important when the user can actually see the thing that is being animated. When Animation component is culled it won't do anything: it won't update animation states, execute events or sample animations.

Always Animate- Animation culling is disabled - object is animated even when off screen
Based On Renderers- Animation is disabled when renderers are not visible.
Based On Clip Bounds-Animation is disabled when Animation. local Bounds are not visible.
Based On User Bounds-Animation is disabled when Animation .local Bounds are not visible.