It can be because of the resources they have at their disposal. Of course he's important. He owns half the town. Sometimes people are important because of the value they are given by others. A movie star is important to his or her fans and children are important to their parents.
Success is more concerned with outcomes.
A successful person is one whose efforts have yielded positive and desirable results. She worked her way through college and law school and is now managing partner of the biggest firm in the city. She's a success. He has taught for twenty years and has published seven learned books. He's a successful scholar.