A nonconformist (with lower-case initial letter) is a person who does not act or think in accordance with the generally accepted conventions but insists on acting or thinking differently. (Nonconformists do not conform to (or with) established conventions, rules or practices.)
Nonconformist (with an initial capital) has a more specific meaning. A Nonconformist Church is a Protestant Church which does not follow the beliefs and practices of the Established Church. The word Nonconformist is almost always used in connection with Churches in England, where the Church of England (or Anglican Church) is the Established Church, and the principal Nonconformist Churches are the Baptist Church, the Methodist Church, and the United Reformed Church (which was formed in 1972 with the merger of two other Nonconformist Churches, the Presbyterian Church in England and the Congregational Church).
Nonconformist, either as an adjective or as a noun, may also be used of an individual who is a member of a Nonconformist Church; while Nonconformist beliefs and practices may be referred to as Nonconformism.
The term Nonconformist came into use after the Act of Uniformity (1662), which required all religious services in England to conform to the practices of the Church of England and follow the forms of service laid down in the Book of Common Prayer. The Act of Uniformity, which led to more than 2000 clergymen leaving the Church of England because they felt unable to comply with the Act's requirements, was one of a series of laws, collectively known as the Clarendon Code, which discriminated against those Protestants who refused to subscribe to the doctrines and practices of the Church of England. In 1661, for example, the Corporation Act had barred from holding public office anyone who was not a member of the Church of England - an exclusion which remained in force until 1828. In fact Nonconformists in England were discriminated against in various ways until Victorian times.