When the children of Israel entered the first court of the Tabernacle in the wilderness, the first thing they were confronted with was the altar of sacrifice. The outer court was equivalent with the telestial world in which we live. (see Institute Student Manual, Old Testament - Genesis through 2 Samuel p. 156). So also, when Adam fell and entered the telestial world one of the first things that he was taught was the law of sacrifice.
It is helpful if we put ourselves in the position of Adam to better understand his first sacrifice. He had just come from the Garden of Eden where nothing threatened his life and he did not threaten the life of any other animal. Now he is asked to take an innocent lamb, tie it up, put it on an altar of stone, slit its throat and burn it up.
I think of how I would feel at that time and the first thing that crosses my mind is that, "I don't want to do this." I see the knife as representing my sins which will inflict pain and death upon an innocent creature. And then it dawns on me, what are we all supposed to think before we sin? - "I don't want to do this." However, all have sinned and fallen short of the glory of God, so the knife must inflict pain and death on this innocent creature so that the sinner can see the end result of his sins. How does the sinner feel when he sees the dead lamb lying there? I know how I would feel, horrible, and then it again dawns on me - how are we supposed to feel after we sin? - Horrible.
I would like the results of my sins removed as soon as possible. A fire is put to the wood and the results of my sins are cleansed from the altar - thus the concept of the baptism of fire and the Holy Ghost. At the altar of sacrifice the sinner comes to understand his relationship with his redeemer and how his sins may be cleansed through Christ who is full of grace and truth and the power of the Holy Ghost.
Adam was further taught by the angel that he was to do all that he did in the name of the son. (Moses 5:8) Therefore, we see another sacrifice at the altar, where Adam uses his agency to no longer do his will but the will of God and act as if he were Christ. Thus Adam's will is swallowed up in the will of the Son of God. Adam is well on his way to conforming to the image of the Son. Omni, in the Book of Mormon, declares that our sacrifice, just like the Savior's, is to be our whole soul. (Omni 1:26)
One of the words in Hebrew for sacrifice is "Corban." The essence of the meaning of this word is to draw closer or nearer. In other words, the result of sacrifice is to draw the participant closer to the one for whom he is sacrificing. We see a mother's love as one of the strongest bonds there is in the human family. Is it because of her great sacrifice given out of love for her children? Christ's love for us is beyond our comprehension. Is his love great because of his great and last sacrifice for us?
If this is the case, then when Adam fell which created a breach between him and God, is it any wonder that one of the first law that God teaches Adam is the law of sacrifice to draw him closer to God and help close the breach.
In the Sixth Lecture on Faith, the Prophet Joseph Smith taught that there is a direct relationship between sacrifice and faith,
"Let us here observe, that a religion that does not require the sacrifice of all things never has power sufficient to produce the faith necessary unto life and salvation; for, from the first existence of man, the faith necessary unto the enjoyment of life and salvation never could be obtained without the sacrifice of all earthly things. It was through this sacrifice, and this only, that God has ordained that men should enjoy eternal life; and it is through the medium of the sacrifice of all earthly things that men do actually know that they are doing the things that are well pleasing in the sight of God. When a man has offered in sacrifice all that he has for the truth's sake, not even withholding his life, and believing before God that he has been called to make this sacrifice because he seeks to do his will, he does know, most assuredly, that God does and will accept his sacrifice and offering, and that he has not, nor will not seek his face in vain. Under these circumstances, then, he can obtain the faith necessary for him to lay hold on eternal life."
According to this, if our faith is weak, one of the things that we can do to strengthen it is to sacrifice to help build the kingdom of God.