Apostasy means falling away. An apostate, in Mormonism, is a Mormon who leaves the LDS Church.
Mormons also talk about the Great Apostasy which they describe as the time between the death of the apostles and Joseph Smith's establishment of the LDS church. They teach that during this long period of time the true church was gone from the earth.
Biblical Christianity teaches that there will always be believers on earth. The true church consists of believers, so it will always have a presence.