If you are studying P of F I assume you are a 'pilot' and not a 'scientist' or 'aeronautical engineer'?
If you are a pilot, you do not need to understand aerodynamic centre.
As far as I remember, the aerodynamic centre is the point on the chord line where clockwise and anti-clockwise aerodynamic moments are balanced.
As you say in your post, this point does not change with angle of attack so provides a constant point of reference.
This may be of interest to an aerodynamicist or designer but is of little use to a pilot.
I generally enjoy the technical side of flying but have never seen the relevance of aerodynamic centre to my understanding of handling techniques.
On the other hand, knowledge of the movement of centre of pressure with angle of attack underpins the understanding of handling during slow flight.