The word apostasy comes from the greek word apostasia which designates a falling away or an standing off from something. According to the Mormon Church, the church that Jesus had began during his earthly ministry (c. 30 AD) had fallen away from the initial teachings and lost it's correct structure. This falling away is a necessary condition for the Mormon Church to claim to be the only true church on the earth, as all of the other ones are wrong.
 Criticisms of the Apostasy
 Matthew 13:24-30, 36-43
Here Jesus tells a parable which poses a serious problem for the LDS conception of a universal apostasy. A farmer plants good seed in his field and an enemy comes along later and plants tares among the good seed. When it becomes evident that this had taken place the workers ask the farmer if they should remove the tares. They are instructed to wait until the harvest so that they do not accidently uproot any wheat. At that time they will gather the wheat into the bundles and burn the tares in the fire.
In verses 36 through 43 Christ's disciples ask for an explaination. The parable, we find, illustrates a great truth about the sons of the Kingdom (the good seed) and their presence on earth (the field). Even though the sons of the evil one (the tares) are present on earth (the field) they do not run out any sons of the Kingdom at any point in time. Rather they grow up together on the planet (the field) until the end of the world (harvest time).
The problem becomes evident when you begin to look for a universal apostasy (i.e. a point in time where there were only tares and no wheat on the field).
 Matthew 16:18
Speaking to Peter, Jesus says that he will build his church and the gates of hades will not prevail against it. Certainly Jesus would have been wrong to make such a claim if the church which he built would drift away completely within the next century or so.
 Ephesians 3:21
Paul's brief doxology here ascribes glory to God in his church to all ages, world without end. In order for God to receive glory from his church, that church must first exist; and in order for that glory to be unto God to all ages that church must continue to exist in all ages. The LDS scheme places a time gap that can not be reconciled with this biblical truth. There were certainly many ages that came and went between the end of the early church age and April 6th, 1830.
 See also
- The Great Apostasy in The Church of Jesus Christ of Latter-day Saints (Wikipedia) - Note: Articles on Wikipedia related to Mormonism are usually dominated by Mormon editors
- How Great Was The Apostasy?
- The Christian Apostasy (DOC) - What happened to Christ's church after the early apostolic era?