What is the part of total fitness that helps a person perform activities well?

There is not just one part of fitness that lets people perform daily activities well...fitness is much more than that. If you want daily activities to be easy you need to weight train, and improve your cardiovascular endurance. This means weight training 2-3 times a week, and doing some sort of cardio 4-6 days a week....if you can manage this, you will improve your performance not only in everyday activities, but in sports, and other fitness related components of your life.