Dry, high altitude, atmospheric air enters engine, is compressed, passed through packs to cool and regulate the pressure and then passed into the cabin.
Passengers breath in dry air, and breath out humid air (that's why you need to drink more while flying - you are expiring moisture and need to replace it).
That moist air eventually moves towards the outflow valve at the rear of the aircraft - but on the way it rubs against the cold aircraft skin, the moisture condenses and either freezes as ice or soaks the insulation.
A better solution than installing moisture extraction fans would have been to using insulating material that does not absorb or is impervious to condensation in the first place.
You can't beat physics, my friend! When warm moist air meets cold, water condenses - it's not a property of the insulation, it's a property of water! Insulation works by preventing cold air from moving - it's difficult to stop air moving without stopping water moving.
This system dries the air before it gets to the cold section and returns some of the water to the cabin air and exhausts the rest of the water overboard.