Difference between linear and non-linear breakdown frames:
Linear frames are a transformation from one key pose to another, basically a shape-changing into another. Non-linear frames create unique shapes for the breakdown frame. The first pose transforms into the second pose with an additional pose in between.
How creating a unique breakdown frame works in animation:
The shape breaks down the animation to create an exciting movement. This is why they call it a breakdown frame.
I made a shape to shape transformation animation where a square gets cut into a triangle:

I also made an animation of a square becoming a circle that has anticipation at the start:
