There is certainly more than one way to answer this question. Historically, an Anglican was a faithful member of the the global Anglican Communion. In the more modern sense, an Anglican is member of the orthodox branch of historical Anglicanism. Primarily though, we are Christians rooted in Scripture, theology, and history.
Christianity reached the British Isles as early as 67 AD, but an official evangelistic mission was commissioned in the 6th Century. In 597 AD, St. Augustine of Canterbury was named the first archbishop of Canterbury in present day England. The English church was almost always considered by the English monarch to be a separate branch of Christianity apart from Rome. The Magna Carta confirms this hundreds of years (1215 AD) even before the Reformation.
KING HENRY VIII
Though best known for his six marriages, King Henry VIII had an important role in the formal establishment of the Church of England as a distinct institution apart from Rome. He declared that the earthly sovereign leadership of the Church of England lay in the British monarch, not Rome. Though his motivation for the split is infamous, the fruits of his labor helped to firmly establish the Reformation in England during the peak of theological reform on the continent.
Archbishop of Canterbury, Thomas Cranmer, was the leader of the Church of England for a significant portion of the English Reformation. He produced the first versions of the Book of Common Prayer as a replacement for the Roman Missal. Upon King Edward's succession to the throne, Cranmer pressed for even more radical forms of theological reform in the church, which ultimately led to our Anglican confession, The Thirty-Nine Articles of Religion.
Christ instituted two sacraments, and orthodox historical Anglicans continue to administer them today to God's people. The Sacrament of the Eucharist (Lord's Supper) is conducted at every Sunday worship service, and is open to all baptized believers. The Sacrament of Baptism is the second sacrament that the Church is called to administer as a form of Christian initiation into the covenant body of believers. God uses both sacraments as a means of grace for his beloved. The sacraments serve as visible signs of inward grace.
Anglicans have a distinctive way of worship that can be traced back to the early formalized church. We get our particular liturgy from the Book of Common Prayer, where we utilize a worship service that is infused with Scripture throughout, climaxing in both the Word and Sacrament. The Anglican liturgy provides us with many benefits in our worship, but one of these ways is in global unity. When we use the BCP in worship, we do not do it alone. We are worshiping in kind and unity with our Anglican brethren across the globe.
Anglican polity is an ancient one. It is episcopal in nature, which is traced back to the very early and primitive Church. Anglicans have bishops, which serve as overseeers of a group of churches in a particular region or affiliation. These bishops elect and serve with an archbishop who represents a particular Anglican province (ours being the ACNA) to the larger global Anglican body (Anglican Communion or GAFCON). Under the bishops on the local level, priests and deacons lead and serve the Church and God's people.