Well historically, a noseband was used on Calvery horses to protect the nose when the horse fell or went face first into the ground. (Or so I read in a few articles) also it makes the horse look good. 😉
A noseband should be snug and be able to fit 2-3 fingers. I prefer to have it looser... just a preference. Purpose is to help keep the horses mouth closed but it doesn't do much, that's what a flash would do or a figure 8 bridle.