This phrase refers to the president of the church, who is also called the “Prophet, Seer, and Revelator.” Mormons believe he, and he alone, receives direct revelation for the entire church. His words take precedence over past prophets and even over written scripture.
The role is a lifetime position, passed to the apostle with the longest tenure upon the death of the current president. Members are regularly reminded that their safety lies in following the living prophet’s words. Great blessings are promised to those who obey, while warnings are given to those who disregard his counsel.