In its broad meaning, revelation is divine guidance or inspiration; it is the communication of truth and knowledge from God to His children on earth, suited to their language and understanding. It simply means to uncover something not yet known. That religion depends on revelation is nothing new.
The Bible illustrates different types of revelation, ranging from dramatic visions to gentle feelings — from the “burning bush” to the “still, small voice.” Mormons generally believe that divine guidance comes quietly, taking the form of impressions, thoughts and feelings carried by the Spirit of God.
Most often, revelation unfolds as an ongoing, prayerful dialogue with God: A problem arises, its dimensions are studied out, a question is asked, and with sufficient faith, God leads us to answers, either partial or full. Though ultimately a spiritual experience, revelation also requires careful thought. God does not simply hand down information. He expects us to figure things out through prayerful searching and sound thinking.
Church leaders are blessed with revelation in their capacity as Church leaders, just as individuals are enlightened in the context of their own lives. Revelation permeates the entire Church — bottom, top and in between.
Individual members are encouraged to independently strive to receive their own spiritual confirmation of guidance given by Church leaders. Moreover, the Church exhorts all people to approach the gospel not only intellectually but with the intellect and the spirit, a process in which reason and faith work together.
For a deeper understanding of the Latter-day Saint principle of revelation, read "Divine Revelation in Modern Times".
In the video below, Church apostle Jeffrey R. Holland addresses the Church's belief in continuing revelation.