Being formal is all about being taken seriously. If you're invited to the White House, you'll want to make a good impression, so it's a good idea to adopt a generally formal demeanor. No jeans or trash talking allowed.
In our casual world, there are still many times we need to be formal, like at weddings or funerals. Adopting a formal manner — i.e., dressing up and not eating with your hands — will help you make a good impression on job interviewers or future in-laws. Being formal doesn't have to mean being stiff or unnatural; it's basically just using good manners and following the rules.