Why Do Clothes Wrinkle?

I think the only good thing about old permanent press fabrics is that they tended to disintegrate pretty quickly so you never had to wear them for long. They were itchy, smelly, and toxic, thanks to the presence of formaldehyde in the treatment that made them wrinkle-free (much like flame retardant clothing in those respects). Of course, modern wrinkle-free fabrics aren't nearly as heinous as their predecessors. Advances in polymer chemistry have led to significant improvements.

The key to both the cause of wrinkling and its solution lies in understanding chemical bonds. Wrinkles form when you break chemical bonds within fabric polymers and then reform them when the fabric is crumpled up. You can break bonds by heating fabric. Other polymers use hydrogen bonding, so getting those materials wet allows the hydrogen bonds in water to restructure the molecules. When you press clothes with a steam iron, you have both heat and water, so you can effectively remove wrinkles. Usually you can prevent them from forming in the first place, even with non-permanent press fabrics, by using a dryer with a cool down cycle and making sure the dryer runs long enough that your clothes are completely dry before the cycle stops.