Ralph Waldo Emerson's essay "Self-Reliance" is a major statement of the beliefs of the Transcendentalist movement. One of these beliefs is that God is present in all things and that all things are connected together by the fact that they are all parts of what we tend to think of as God.
Therefore, in the quote you cite, the divine idea is God. Each of us represents that divine idea because each of us is a part of God.
Because of this belief, Transcendentalists were often early advocates of women's rights and the abolition of slavery.