Anglicanism (or Episcopalianism) is a kind of irenically Reformed Protestant Christianity. More specifically, it is a kind of Reformed and Evangelical Catholicism within the English branch of the Western Catholic Church.

That's a mouthful. What does this mean? It means that Anglicanism is a way of following Jesus that may be for you, and that allows you to live a very full, rich, and beautiful faith centered around common prayer.

Getting into it, Anglicanism is:

Irenic

Anglicanism is irenic, which means that it seeks peace amongst Christians of various views, both within, and without. The back-and-forth tumult of the English Reformation led to, by necessity, both compromise as well as much finding of nuance and theological subtlety. The need for a national church that could handle the diversity of opinion and contention in Reformational England demanded this kind of irenic approach, which led to a generously irenic church.

In practice this has meant:

1. Anglicanism has, unlike some other Christian traditions, never claimed to be the 'one true Church'. Instead it sees itself as part of the larger Body of Christ.
2. Likewise, Anglicanism has been particularly willing to grant the validity (even with disagreements) of other parts of the Body of Christ. See, for instance, Richard Hooker arguing that the Roman Catholic Church is, whilst in error, still a part of the church whilst still steadfastly affirming the Reformed and Protestant theology and doctrines of the Church of England.
3. Within Anglicanism itself there has always been a relatively greater degree of leeway and freedom of conscience regarding theological matters than some other traditions.

This does not mean that Anglicanism has no specific doctrine or teachings, or that it is truly a big tent where anything goes so basic creedal orthodoxy is maintained. It does mean, however, that the English Church and its tradition have an undoubtedly irenic nature.

Reformed

Anglicanism is Reformed and Evangelical. This means that the English Church, as part of the larger Protestant Reformation, has reformed itself away from accumulated erroneous doctrines that had served, under Rome, to obscure the heart of the Gospel of Jesus Christ. Anglicanism keeps at its center a grace-filled, Biblical approach to doctrine.

Reformed features:

1. The primary, clarity, and sufficiency of Scripture. IE: Sola Scriptura, see Article VI.
2. Justification by faith alone. IE: Sola Fide, see Article XI.
3. A Reformed sacramental theology. Emphasis on the Sacraments being an "outward and visible sign of an inward and spiritual grace given unto us, ordained by Christ", plus an emphasis on our receiving the benefits of the Sacraments by faith.
4. Another side of Sola Scriptura, we don't hold ecumenical councils or church decree to ever be infallible, and hold only the Bible to be an infallible authority. IE: the Church can err.

And more things besides.

Catholic

Anglicanism is Catholic. This doesn't mean Roman Catholic (as that part of the church likes to say that only it is Catholic). For the Divines of the English Reformation, Catholic meant as confessed in the Apostles', Nicene, and Athanasian Creeds. IE: the One Church. The One Faith. The undivided faith. The word "Catholic" itself comes from the Greek kata holos, which meant "according to the whole."

So, when we say we are Catholic, we are saying that we are part of Christ's One Holy Catholic and Apostolic Church, that we have continuity with the historic church and its Apostolic teaching and doctrines.

Practically, this means that:

1. We affirm the Apostles', Nicene, and Athanasian Creeds.
2. We affirm Nicene Trinitarianism and Chalcedonian Christology: Jesus is fully God and fully Man.
3. We maintain the threefold order of Bishops, Priests, and Deacons, and the historic Episcopate, with tactile ordination and the laying on of hands symbolising the continuation and succession of Apostolic teaching through time. IE: we are Epsicopalians.
4. We maintain liturgical worship, reverence toward the departed Saints and Martyrs and Fathers, and maintain various historic traditions and practices of the Church.
5. We accept as doctrine, the general teachings of the first four Ecumenical (or General) Councils (though not infallibly so, see Article XXI).

Built around Common Prayer & the Daily Office

A central feature of Anglicanism is its emphasis on common prayer, and specifically common prayer through one of the many versions of the Book of Common Prayer (also called the Prayer Book or the BCP). The BCP is essentially the service book containing the liturgies and prayers of an Anglican church.

The Episcopal Church uses the 1979 BCP. The Church of England's 1662 BCP is the last BCP of the Church of England, and essentially all subsequent BCP's reflect this, and so for this and other reasons, it stands centrally among the historic formularies of the Anglican communion. IE: reflective, in some capacity, of the theology of Anglicanism generally.

The specifics and details of the BCP are for another article, but what this emphasis means is:

1. Lay accessibility. Anglicanism rather uniquely emphasizes the accessibility of liturgy and prayers of the church, essentially approaching these things with a Reformational and democratising attitude. Particularly, layity are empowered to pray the Daily Office (see below).
2. The Prayer Book is doctrine. Anglican churches doctrine is set partially in their prayers and liturgy. This is a priniple called Lex Orandi, Lex Credendi - "the law of prayer is the law of belief."
3. The Daily Office. Anglican churches have adapted the Canonical Hours of medieavel monasticism into the Daily Office (specifically Morning and Evening Prayer -- also called Mattins and Evensong), which can be prayed by anybody as part of their private devotions, or in a corporate setting of worship.
4. Unity. Common prayer is a unifying force for disparate threads across both the Communion and in individual churches.

Further Reading

• » Anglicanism: A Love Letter by Rev. Ben Crosby
• » The Book of Common Prayer (BCP): A Rookie Anglican Guide to the Prayer Book