From a Catholic perspective. The simplified or catechetical version:http://www.ewtn.com/faith/teachings/chura1.htm
The Catholic Church is the Mystical Body of Christ
by Fr. William G. Most
Speaking of full membership in the Church, Pius XII, in his Encyclical on the Mystical Body, said it is the society of those who have been baptized, and who profess the faith of Christ, and who are governed by their bishops under the visible head, the Pope, the Bishop of Rome.
The Church came into being when Christ died on the Cross, but it was formally inaugurated on Pentecost, when He sent the Holy Spirit as He had promised. St. Paul speaks of all Christians as members of Christ, so that with Him, they form one Mystical Body (Cf. 1 Cor 12:12-31; Col 1:18; 2:18-20; Eph. 1:22-23; 3:19; 4:13). St. Paul did not use the word Mystical. It was developed more recently to bring out the fact that this union is unique, there is no parallel to it. It is not the same as the union of a physical body, nor that of a business corporation.
The Church, the Mystical Body, exists on this earth, and is called the Church militant, because its members struggle against the world, the flesh and the devil. The Church suffering means the souls in Purgatory. The Church triumphant is the Church in heaven. The unity and cooperation of the members of the Church on earth, in Purgatory, in Heaven is also called the Communion of Saints. When St. Paul uses the word "Saints" in opening an Epistle, he does not mean they are morally perfect. He has in mind Hebrew qadosh, which means set aside for God, or coming under the covenant. Being such means of course they are called to moral perfection. But of course, not all have reached it in this world.
The word "Saint" in the modern sense means someone who has been canonized by the Church in recent times, or was accepted as such by the Church in earlier times. If a person is shown to have practiced heroic virtue--beyond what people in general do - in all virtues, the title "Venerable" is given; with two miracles by that one's intercession, the title is "Blessed"; two more miracles can lead to canonization and the title of Saint.
Taken from The Basic Catholic Catechism
PART FIVE: The Apostles' Creed IX-XII
Ninth Article: "The Holy Catholic Church; the Communion of Saints"
By William G. Most. (c) Copyright 1990 by William G. Most