Connection is literally the process of uniting body parts.
It is the most basic and simplistic concern.
Instead of moving your arms via the shoulder or relying upon local muscle strength, you 'connect' the arms to the back and move via the torso and legs instead. Maintaining connection when performing different tasks is a major undertaking for the new student.
It is not enough to do a movement.
You must move in a whole-body manner.
The hardest part of this requirement is to remain relaxed but not floppy, flaccid or crumpled.