Utmost means "the greatest extent or amount." When you work as hard as you possibly can, you do your utmost to accomplish your goal.
Whenever something is the most, it can be described as the utmost. If a message is of the utmost importance, it's as important as it possibly can be. Any time you want to really want to emphasize that you believe in something more than anything else or truly intend to do something, do your utmost to use the word utmost.