“Trust thyself: every heart vibrates to that iron string” means that if you trust yourself, then you can truly be content in whatever you do or wherever you go.
The metaphor of iron string is the innate independence of man which Emerson (who famed the essay, "Self-Reliance") has established as intrinsic to man earlier in his essay as he alludes to man's infancy and youth which conforms to no one and expresses his young man without compunction. Emerson is very much a truthful man (at least that is what he preaches) and he trust himself in what he says.
He believes that you should always speak the truth because that is the only way you can be true to yourself. By trusting yourself, then your heart will not ache with guilt and your conscience will not tear your mind. When you can trust yourself you are living in a state of peace and your heart vibrates like a string on a guitar, making music pleasing to the ear and the body.
The path to self-reliance may seem a bit daunting if you’re not sure where to start. It takes a bit of getting used to, but it’s usually not all that hard. Check out some tips to help you start on a more self-reliant path at Survivalathome.com.