Heavenly Father
Our Heavenly Father's mission, or purpose, is the bring us back into his presence. John 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. Moses 1:39 For behold, this is my work and my glory—to bring to pass the immortality and eternal life of man.
Jesus Christ
Jesus Christ's purpose is to glorify the Father and fulfill his purpose: 3 Nephi 27:13 "Behold I have given unto you my gospel, and this is the gospel which I have given unto you—that I came into the world to do the will of my Father, because my Father sent me."