Purgatory refers to a doctrine in the Roman Catholic Church which posits that those who die in a state of grace undergo a purification in order to achieve the holiness necessary to enter heaven (Catechism of the Catholic Church 1030).
The Orthodox Church has neither explicitly recognized the term "purgatory" nor officially accepted such a state, which is distinct from the more general being "asleep in the Lord." That said, Eastern Orthodox Bishop Kallistos Ware acknowledges several schools of thought among the Orthodox on the topic of purification after death. This divergence indicates that the Catholic interpretation of purgatory, more than the concept itself, is what is universally rejected. Also, there are Orthodox sources that indicate some sins can be forgiven after death;(Mt 12:32) but which also reject the notion of purgatory because of the indulgences and idea of purgatorial fire that are tied to it.
Some Eastern Orthodox sources, including the Ecumenical Patriarchate, consider Purgatory to be among "inter-correlated theories, unwitnessed in the Bible or in the Ancient Church" that are not acceptable within Orthodox doctrine, and hold to a "condition of waiting" as a more apt description of the period after death for those not borne directly to heaven. This waiting condition does not imply purification, which they see as being linked to the idea "there is no hope of repentance or betterment after death." Prayers for the dead, then, are simply to comfort those in the waiting place.
Other Orthodox believe in the "toll gate" theory by which the dead go to successive "toll gates" where they meet up with demons who test them to determine whether they have been guilty of various sins during life and/or tempt them to further sin. If they have not repented and been absolved of those sins, or if they give in to sin after death, they will be taken to Hell.