Question: "What is the Anglican Church, and what do Anglicans believe?"
Answer: The roots of the Anglican, or English, Church go back as far as the 2nd century, but the church traces its current structure and status back to the reign of King Henry VIII, who ruled from 1509 to 1547. The events that led to the formation of the state Anglican Church are a curious mix of ecclesiastical, political, and personal rivalries. Henry petitioned Pope Clement VII for a divorce from Catherine of Aragon, but was denied. When Protestant Thomas Cranmer became Archbishop of Canterbury, Henry saw his chance to bypass the Pope's authority and get what he wanted. In 1531, Henry manipulated the English clergy into accepting him as head of the church in England. In 1532, Henry forced the national convocation to agree in The Submission of the Clergy that they would not promulgate any papal bull in England without the king's consent. In 1534, Henry led Parliament to pass a series of laws depriving the Roman Catholic Church of any authority in England. The Act of Supremacy declared the king to be “the supreme head of the church in England,” thus giving Henry the same legal authority over the English church that the Pope exercised over the Roman Catholic Church.
Though the English church didn't assert total independence from Rome until Henry VIII's reign, there had been aspects of independence throughout its history. The Celtic branch, founded by Saint Patrick in Ireland in 432, borrowed certain practices from the ancient Druids, and never was fully under papal authority. The Saxon branch, founded by Saint Augustine in 597, was under papal direction, but not without resistance. The various tribes of England had never fully submitted to Roman occupation, and when the Roman Legion was withdrawn, the Saxon church continued on an independent course. These two branches spread across the land, often clashing over territory and authority, until King Oswey of Northumbria called the Synod of Whitby in 664. This synod merged the two churches nominally under the Roman Catholic Church and laid the groundwork for Henry's acts nearly 900 years later.
The doctrine of the Anglican Church is an interesting mix of Catholicism and Protestant Reformation theology. The Apostles’ Creed and Nicene Creed are authoritative declarations of belief for the Anglican Church and are typically recited in worship services. Interestingly, the church does not require individuals to agree with or accept all the statements of those creeds but encourages its members to join in the process of discovery. The 39 Articles, developed in the reign of Elizabeth I, laid out the Protestant doctrine and practice of the Anglican Church, but were deliberately written to be so vague that they were open to various interpretations by Protestants and Catholics. As in the Catholic Church, the celebration of the Eucharist is central to the worship service, along with the communal offering of prayer and praise through the recitation of the liturgy. In all liturgical churches, there is a danger of allowing the form of religious ceremony (Isaiah 29:13) to replace the personal application of faith (Psalm 51:16-17). This was a key point of contention by the Puritans and others who ultimately left the Anglican Church. Thomas Shepherd, who was expelled from the Anglican Church in 1630 for non-conformity, was a spiritual giant who was concerned that people distinguish between the work of grace in genuine conversion and the religious pretense that was common within the church. (Shepherd was one of the pivotal men in the founding of Harvard College and became a mentor of Jonathan Edwards, who was mightily used of God in the Great Awakening.)
The Anglican Communion has 80 million members worldwide in 38 different church organizations, including the Episcopal Church. The Archbishop of Canterbury is the recognized spiritual head of the church, though each church organization is self-governing under its own archbishop. In addition to those churches, the Continuing Anglican Communion, established in 1977, is composed of churches which share the historic Anglican faith, but reject the changes in the Episcopal Book of Common Prayer, as well as the ordination of women and gays/lesbians to the clergy, and have thus severed their ties with the main church.