In Emerson's thought, to become a "man" means to reach one's true or highest potential. Emerson, who is addressing young men just out of college, draws a distinction between merely entering adulthood and finding one's highest destiny.
The person who reaches his highest potential can only do so by not conforming to a preset plan for his life. It can be easy to step into the role, for example, of taking over the family farm or business or of following a family tradition of entering law school. A true man, however, does not simply unthinkingly follow someone else's plan. Instead, as the essay lays out in some detail, one must do the harder work of looking inward. What does your soul tell you it wants you to do? What makes the iron string of whoever you are "vibrate" with longing? This is the path to follow.
The divine force has a destiny for every person, and it is up to that individual to find it. Following this destiny is most often going to mean not conforming to what other people, family, or society thinks is the safe, secure, and acceptable path.
Emerson points to people such as Jesus, Buddha, and Galileo as individuals who did not conform. By following their inner destinies, they changed society in profound ways. Emerson urges his audience to take the harder path, just as they did, as this will lead to the greater good.