You had to dampen starched fabric (in fact we always dampened EVERYTHING we ironed) because you couldn't get the wrinkles out if you didn't. You sprinkled the clothes with water (we didn't have a pop bottle sprayer - we just dipped our fingers in a bowl of water and shook our hands over the clothes to shake off the water), then folded and rolled the item in a neat little package and, put them all in a laundry basket and let them sit for a while so the water distributed itself in the fabric so it was evenly dampened all over, then we could iron. They came out looking better than new!
A lot of women would refrigerate anything that was starched and dampened before ironing if she thought she may not be able to get to the ironing before a certain length of time went by. Dampened UNstarched clothes would just dry out if left too long, but dampened starched fabric could get moldy or buggy if left too long. Refrigerating eliminated that possibilty.
I still dampen and iron 100% cottons before I cut them.
This is probably more than you ever wanted or needed to know about starching/dampening, but there you go. You probably also know how OLD I am!