Prayer Unlocks Power

When the prophet Alma in the Book of Mormon began seeing waywardness and wickedness in his son, he turned to prayer to engage God in the struggle for his son's soul. In response to the faith-filled prayers of Alma and the people of the church, the Lord sent an angel to halt Alma Junior on the path to destruction. The young man recorded the words of the heavenly messenger thus:

And again, the angel said: Behold, the Lord hath heard the prayers of his people, and also the prayers of his servant, Alma, who is thy father; for he has prayed with much faith concerning thee that thou mightest be brought to the knowledge of the truth; therefore, for this purpose have I come to convince thee of the power and authority of God, that the prayers of his servants might be answered according to their faith.
--Mosiah 27:14

Prayers on behalf of others work. They unlock the power of God. They don't necessarily change God's will, but they have an impact. 

Things happen with prayer that might not happen or might happen differently without prayer. I do not understand completely how it works or why it works, but I am convinced by many evidences that prayer for others does indeed work.