Drawing convincing clothing and folds can add a lot of realism and believability to a drawing. Like a lot of things, when an artist draws them well you don't even notice them; you only notice when they're drawn poorly.
The Famous Artists Course that I own has a great chapter on drawing folds. Here it is, in its entirety (again).
Even if you're not drawing men wearing shirts and jackets, or women wearing skirts, the same principles apply.