Let's take a closer look at the full quotation from Emerson:
Trust thyself: every heart vibrates to that iron string
Emerson explains fairly explicitly what he means by this comment. In writing on the virtues of individualism and self-reliance—virtues which had been championed by various previous poetic movements, including Romanticism—Emerson is stipulating that we must trust ourselves because each person's heart "vibrates" according to one's own values and determination. The "power" within each person, a power which sets the string of one's heart trembling, is completely different to any power that has previously existed in any other person. Emerson uses musical imagery to underscore this fact: just as a string will vibrate to a different pitch depending on how loosely or tightly it is tuned, and will sound differently depending on the "power" with which it is struck, each person makes a different impact upon the world and is guided by one's own particular sense of self.