The fan is not very conspicuous ~ roll binding would be a better name!
The aim of fan ~ roll ~ binding is to place the thinnest possible strip of glue as the hinge of every page. This is done by securely gripping the squared-up fore edge of the loose sheets ~ then rolling the pages around themselves in such a way that they are spread out by a tiny fraction. After straighteng the sheets out and applying approriate pressure ever sheet will be securely glued to every ther one.
Without the rolling ~ fanning ~ the glue would only stick onto the very edge of each sheet. This could be called no-fan binding. It is used ~ but is unreliable.
If it is possibe to roll the paper clockwise ~ then glue ~ then roll it anticlockwise ~ and glue again ~ then the binding is even more securethnan with a single roll ~ hence we have double fan binding ~ or double fan binding.
I plan a visual demonstration here - but until that is prepared try browsing over to a demonstation [1275511].