Here we can see the distance traveled (Actual Path) is AB + BC, but displacement is AC.
where, AC = AB + BC.
Now, What is Angular displacement?, In simple words we can say displacement covered in terms of angle.
Thus the displacement of the body moving in the curved path is represented by Angular displacement.
or
It is defined as the angle in radians through which a point has been rotated about a specified axis. It is the distance an object moves in a curved path. It is represented by the length of the arc of curved path.
The arc is measured in the angle and hence angular displacement is also measured as an angle.

The angular displacement is represented in polar co-ordinates and not in x-y co-ordinates.

Let''s say, a body is moving in circular direction as shown in fig,

For $\theta$ angle and the radius of curved path is r. The linear displacement is related to the angular displacement as: S = r $\theta$ ...............(1)where r = radius of the curvature,
$\theta$ = angular displacement.
The equation (1) is the angular displacement equation.

Here we can see the distance traveled (Actual Path) is AB + BC, but displacement is AC.
where, AC = AB + BC.
Now, What is Angular displacement?, In simple words we can say displacement covered in terms of angle. 
Thus the displacement of the body moving in the curved path is represented by Angular displacement.
or
 It is defined as the angle in radians through which a point has been rotated about a specified axis. It is the distance an object moves in a curved path. It is represented by the length of the arc of curved path. 
The arc is measured in the angle and hence angular displacement is also measured as an angle.

The angular displacement is represented in polar co-ordinates and not in x-y co-ordinates.

Let''''s say, a body is moving in circular direction as shown in fig,
 
For $\theta$ angle and the radius of curved path is r. The linear displacement is related to the angular displacement as: S = r $\theta$ ...............(1)where r = radius of the curvature,
$\theta$ = angular displacement.
The equation (1) is the angular displacement equation.