Long ago, prophets, the spokesmen of God, were called to warn the people of dangers that would come upon them if they did not change their ways. There would be some that would listen, but over time, most would not. The prophet would then be killed, the city of people would be destroyed and/or would suffer in unusual ways. This pattern was set from the beginning of the world. God would call a prophet, the people wouldn't listen after a while, and they would reject the words of the prophet. This rejecting of the words of God is called an Apostasy.
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It's called the Great Apostasy because it was the greatest period of time when the gospel wasn't on the earth. The some of the apostles had talked about his when they wrote their epistles. Concerning the second coming of Jesus Christ, Paul said, "Let no man deceive you by any means: for that day shall not come, except there come, a falling away first" (2 Thessalonians 2:3). That "falling away," or apostasy, did happen. It is no coincidence that this time in our world's history is known as the Dark Ages. There was no light of the Gospel to bring people closer to Heavenly Father and Jesus Christ.
"For [Christ] is the same yesterday, today, and forever; and the way is prepared for all men from the foundation of the world, if it so be that they repent and come unto him" (1 Nephi 10:18).