In brief, the one, undivided Church is said to have begun on the day of Pentecost, 50 days after the Resurrection of Christ. Already by the 4th century the term "Orthodox Christian" was used to designate those Christians who remained faithful to the totality of the teaching of Jesus Christ and the apostles, as opposed to those who were known as "heretics" who promoted false doctrines and beliefs. [The term "orthodox" means "correct believing" or "correct, true glory."]
Due to a variety of complex circumstances, the Western church, known today as the "Roman Catholic Church," split from the Eastern Orthodox Patriarchates of Constantinople, Jerusalem, Alexandria, and Antioch in the 11th century. Roman Catholics, however, see it from the opposite perspective, namely that the Orthodox Church broke communion with the Roman Catholic Church.
We Orthodox believe that we are the continuation of the ancient Orthodox Christian Church, that we trace our history back to Christ and the apostles, and that the Church was "formally" established on the day of Pentecost. The Roman Catholic Church placed itself outside of this fellowship when it broke off communion with us in the 11th century.
This is a very brief outline; a thorough treatment of the issue would fill volumes, and there are many resources readily available should you wish to research the history of this further. For more information I would recommend that you check links on Church history. Or you may wish to read the book by Metr. Kallistos [Timothy] Ware called "The Orthodox Church," which gives the historical background in detail.
For further reading:
Metr. Kallistos Ware's books and Fr Thomas Hopko's books are available from booksellers and from: