how do they work? elaborate
They're momentum-based. It works similar to other fans in platforming; the height you get is dependent on how much vertical momentum you have when going in. If you're already in the beginning of a jump when you enter your fan, it'll boost your jump significantly, allowing you to reach higher places where the highest possible jump alone, or the highest point on the fan alone, wouldn't let you access.
TL;DR: Start your jump as you enter the fan's range to get the biggest boost.