a lot of things.

more space, you can upload more file types to your page, if you have a paid domain with premium hosting plan you won't have the banners/ads you will eventually have on your site if your site right now is the Free subdomain with free hosting


you also have the ads if you have a domain with free hosting

Depends in part on the purpose of your site.

A domain does not bind your site address to a particular hosting company. Also the email address is not bound to a particular email service.

Domain names are more memberable and attract type in traffic.

For a business a sub domain at a hosting service simply lacks credibility.