John Taylor wrote the book Mediation and the Atonement when he was President of the Church. It was one of his main contributions as president. He wanted the Saints to understand the Atonement, and his book is a classic. For inclusion in The Encyclopedia of Mormonism, Elder Jeffrey R. Holland wrote the article on Atonement, but Elder Holland humbly told us as the editors, "I can’t do any better than just to quote John Taylor."
Here is one of President Taylor’s comments:
The Savior thus becomes master of the situation—the debt is paid, the redemption made, the covenant fulfilled, justice satisfied, the will of God done, and all power is now given into the hands of the Son of God—the power of resurrection, the power of redemption, the power of salvation. … He becomes the author of eternal life and exaltation. He is the Redeemer, the Resurrector, the Savior of man and the world. (p. 171)
And here is another comment, from a different chapter:
In some mysterious, incomprehensible way, Jesus assumed the responsibility which naturally would have devolved upon Adam; but which could only be accomplished through the mediation of Himself, and by taking upon Himself their sorrows, assuming their responsibilities, and bearing their transgressions or sins. In a manner to us incomprehensible and inexplicable, he bore the weight of the sins of the whole world; not only of Adam, but of his posterity; and in doing that, opened the kingdom of heaven, not only to all believers and all who obeyed the, law of God, but to more than one-half of the human family who die before they come to years of maturity, as well as to the heathen, who, having died without law, will, through His mediation, be resurrected without law, and be judged without law, and thus participate, according to their capacity, works and worth, in the blessings of His atonement. (p. 148–149; emphasis added)As President Taylor undoubtedly knew, King Benjamin said many of the same things: "Believe that man doth not comprehend all the things which the Lord can comprehend” (4:9). We can know many things. We can understand the symbolism, we can understand the fulfillment of prophecy, we can understand that it’s real and we can feel its reality, but the eternal economy in all of this, we cannot fathom.