The benefits depend on what you are doing. Is it a personal site, a business site, for advertising, for servicing clients/friends/family?
Dynamic is always nice because it keeps your site fresh, even if it's just rotating pictures on the front page. Generally static just means that you have to make any updates manually, or that content doesn't change automatically (such as pulling from a database, or using a scripting language to make changes).
If you want people to visit your site, you want to keep it updated so they have a reason to visit it every day.