The chief ingrediant, and its biggest problem or most attractive feature (depending on whom you ask) is its ability to be all things to all peoples, and has been so since the beginning.
Archbishop Cramner wrote the basis of Episcopalian/Anglican worship, the Book of Common Prayer for King Edward NOT Henry VIII. Henry had made the church in England subervient to him, and had confiscated monastaries, etc. but had no definite program for a church. The Anglican Church basically started as a diocese with the King instead of Pope giving orders (btw, the Queen’s title “Defendor of the Faith” was given by the pope of Rome to Henry VIII for a pamphlet he had written in defense of seven sacraments). But since Henry wasn’t persecuting Protestants as the Latins were doing on the Continent, soon Calvinist, Lutheran and other ideas were floating around in England. When Cramner went about compiling the service book, he had an array of “believers” from those who accepted the king as the head of the church but changed nothing else, to those believed in predesination, denied the Real Presence etc. So the services were based on the rites (i.e. Roman) in use in England at the time, translated into English, and then removing any language that any group on this continuum would object (hence references to the Blessed Virgin, Saints, etc went out, or reworded to be acceptable to everyone). This resulted in some weird combinations, chief being the Anglican continuance of bishops (hence Episcopalian) with a Calvinist theology (Priesthood of All Believers).
Later you got various groups, some moving more Traditional, Catholic (“Anglo-Catholic”) and some going more Protestant. This is sometimes refered to High and Low Church.
The problem is now Episcopalian doesn’t mean anything anymore. There are those who are more Catholic thant the pope, and others more Protestant than Billy Graham. this leads to odd combinations: I once went to a Episcopalian service which was chanted in Gregorian Chant in Latin, where the priest was living with his lover, and most of the congregation were gay.
The Anglican-Episcopalians like to refer to themselves as a bridge, the Western Orthodox or the Catholic Church in England/US. They came up with the branch theory of the Church to explain themselves I guess to themselves, as neither the Latins nor the Orthodox buy it. As the mainstream church has become increasingly liberal various groups are breaking off and getting themselves under conservative bishops in e.g. Africa.
Others have just decided to go East or Swim the Tiber. Some have gone East and Swam the Tiber have taken the BCP with them: in the Orthodox Church there is a Rite with the BCP corrected to agree with Orthodoxy, and their is not exactly a rite but a dispensation in the Latin church with a revision of the BCP called the Book of Worship I believe.