First of all, corset shape and purpose changed a great deal in the early twentieth century, it might be helpful to narrow down the time frame.

They were considered an essential undergarment back then. Aside from aesthetic reasons, corset also provides bust/back supports and anchor for garters (particularly after 1905 or so). Most women have corsets just like most modern women own bras regardless of social-economic class, but poor women's corsets are usually handmade from cheap but sturdy materials and without the restrictiveness of proper corsets.

I remember reading this passage in school, it was from Evidence of a Female Millhand to the Parliamentary Commissioners, a factory worker testified that being too poor to afford a corset (called stays at this time period) and started working at a young age resulted in her deformed back:

"I was about 13 years old when it began coming, and it has got worse since; it is five years since my mother died, and my mother was never able to get me a good pair of stays to hold me up, and when my mother died I had to do for myself, and got me a pair. "

Some men also have worn corsets to give a streamline look, but it never quite caught on.

A really nice source you can cite on is the book Unmentionables by Elaine Benson and John Esten. I can scan some pages for you.

(I'll be back for more specific questions if you have any.)