Hi, Lighting, good question!
Wool has amazing properties to it. It can actually absorb 10 times its weight in liquid without feeling wet at all. This is what makes it work as a soaker (aka diaper cover). Though the inside of the wool soaker is in contact with the wet diaper, the outside of the soaker doesn't feel wet. Of course, if you never change the diaper, the soaker will eventually be wet....it can't absorb forever.
In my experience, the wool soaker still feels dry after being worn all night. In fact, I have heard some moms say that wool is the ONLY way to get their baby through the night without a leak.
The key is the lanolin, which is an oil-like substance secreted by a sheep's skin. Wool labeled "superwash" has had the lanolin stripped from it in order to make the wool machine-washable. That type of wool will NOT absorb liquid and can't be used as a diaper cover.
Wool is also good for diaper covers because it is naturally antifungal and antimicrobial, which means that it won't start to smell bad from its contact with urine. You can actually turn the cover inside out, let it air dry, and use it again at the next diaper change.
That's probably way more info than you wanted!
By the way, what book are you reading that mentioned soakers? I'd like to try to find it and read it too.