Unitarianism is a word with two different and quite distinct meanings. In popular usage, Unitarianism is a common abbreviation for a religious denomination more properly known as Unitarian Universalism. Unitarianism is also a technical term for a theology of God which insists that there is only one divine person, over against the more common (in Christianity) trinitarian theology.
Though it is meaningful to make a distinction between the denomination and the theology, the overlap between them is no accident, and they share some common history. Theological unitarianism became prominent during the Enlightenment, as some Protestant Christians attempted to separate the "true" Christianity from what they considered superstitious later accretions. The essentially mysterious doctrine of the Trinity did not withstand their scrutiny.
In the United States, theological unitarians were a prominent group within the larger Congregationalist movement (itself descended from the Puritans.) Unitarianism was particularly strong in New England, and John Adams, the second President of the United States, was a notable unitarian, as were Thomas Jefferson and Millard Filmore.
In 1825, many Unitarian churches decided to split from the rest of the Congregationalists, and become their own denomination. In the course of the 19th century, the Unitarian denomination became progressively more liberal, though it was not until 1961 that the Unitarian denomination joined with another theologically liberal denomination, the Universalists, forming the Unitarian Universalist Association, though retaining the copyright to the name American Unitarian Association.
Another group, wanting to revert to the former Unitarian theology, attempted to use that name, and eventually agreed to call itself the American Unitarian Council.
In 1995, the main Unitarian-Universalist organization declared officially that it was not part of Christianity.