There is more than one definition of the literary movement of 1836 to 1846 of several New England writers known by that name. It was essentially a religious-spiritual movement expressed in poetry and prose:
Transcendentalism began as a religious concept rooted in the ideas of American democracy. When ... Ralph Waldo Emerson [,] decided that the Unitarian Church had become too conservative, they espoused a new religious philosophy, one which privileged the inherent wisdom in the human soul over church doctrine and law. (enotes Summary)
...they may be defined in a somewhat wider perspective as children of the Puritan past who, having been emancipated by Unitarianism from New England's original Calvinism, found a new religious expression in forms derived from romantic (sic) literature and from the philosophical idealism of Germany (Miller iv).
Ralph Waldo Emerson, and the other main proponents of this philosophy (notably Henry David Thoreau, Margaret Fuller, William Ellery Channing, and Orestes Augustus Brownson) believed that the Unitarianism current in academic and intellectual circles at that time were becoming too much like the entrenched bureaucratic Christianties of Europe (such as Roman Catholicism and the Anglican Church) and less like the kind of religions on which much of New England was founded. It must be remembered that one of the main sources of argument between the Church of England and the Puritans and other New World sects (although by no means the only point of contention) was the self-determination of the faithful's relationship with God. This coincided with the American belief in democracy, and shunned religious hierarchies such as the ones coming into being in the Unitarianism of the time. One of the most famous works of this movement's title supports this; the essay by Emerson entitled "Self-Reliance" explains most of Emerson's, and the movements, main tenets. Essentially it is a religious belief that holds that every human being may find God within the "genius" of his own self; that "trusting thyself' is the most important virtue, and people that are truly self-reliant will find God and follow the right path. Nonconformity should not frighten the faithful from trusting themselves, and everyone has the responsibility to think for themselves. This is a simplification, of course, but Emerson is rejecting the ideas of a received knowledge from outside (such as from a church hierarchy) determining a person's faith in God; Emerson thought this essentially personal and only possible through self-realization. Transcendentalists wrote poetry, too: Thoreau, for example, wrote early in his life of his struggle to find his true self and to relate to God.
I am a parcel of vain strivings tied
By a chance bond together,
Dangling this way and that, their links
Were made so loose and wide,
For milder weather. ("Sic Vita" lines 1-6, Miller 231-2)
Not every transcendentalist was concerned with the same things; while Emerson may have been largely concerned with religion, and Thoreau with the self, Alcott commented on the two other authors, and Fuller wrote about women. But these writers were joined in the spirit of American individualism, expressed mainly in religious terms.
Source: The American Transcendentalists: Their Prose and Poetry. Perry Miller, ed. Garden City, New York: Doubleay Anchor Books, 1957.