When you emulate someone, you imitate them, especially with the idea of matching their success.
When someone is impressive because of their great skills, brains, strength, or accomplishments, others will emulate them. To emulate is to imitate and model yourself after someone. People emulate role models — people they want to be like. After Michael Jordan retired from the NBA, player after player tried to emulate Jordan's game and success. It's hard to be as good as someone like that, but having a hero to emulate can be helpful in many areas of life.