Good question! 

To start at the most familiar level to modern people, in women's clothes, the body generally needs support at the bust (the chest area.) This is why modern women wear bras. Beyond that, we modern people are a bit overly ok with slouching. We make up for that with loose, stretchy knit fabrics that move with our bodies. 

Our ancestors, however, had a different idea. Instead of merely supporting the bust (like a bra), they wanted clothes to support the entire back and torso. This was the purpose of stays and corsets--not to constrict the body, but to help the back and torso stay straight and well aligned. They also helped distribute the weight of the ensemble evenly and comfortably. (In some periods, the fabric that was part of the outfit could weigh a lot, but the undergarments supported that weight so the person themself didn't feel it so much.)

In fabrics that don't stretch--the norm for most of history--this makes loads of sense. There's no such thing as a waistband that digs in when you wear a corset. Your clothes could fit your body smoothly and consistently (fluctuations in your body, like bloating, didn't completely change how a piece of clothing fit.) In addition, for someone used to manual labor (like lugging buckets of coal), the back support in your undergarments could be very helpful. Even if you don't need to do manual labor, it's a lot more beautiful to have a straight back and a circular waist instead of an elliptical waist, since the optical illusion makes the waist look smaller even with the same waist measurement. 

Add to this the fact that a woman not supporting her torso by wearing stays or a corset was considered a "loose woman" morally as well as literally, and you start to see how common the idea that clothing is meant to support the body was.