We're twirling the Longitudinal Center of Gravity, the Sweetspot Plane. The shaft rotates around it, not vice versa. The #3pp attaches to it, defines the top of it on the handle when hitting a shot.
After one year of searching for the answer I believe the twirl is a way to promote a right to left or left to right spinning shot.
Keeping in mind the proper rhythm and alignment, if I twirl the club in a counterclockwise direction it allows me to focus on hitting draw.
When I do the opposite ,clockwise twirl in my set up then it helps me visualize a fade better.
Of course there are much more factors involved but these are the generalities.