Israel are commanded time and again not to eat or drink any blood. This strict prohibition is repeated many times in the Torah. For example, in Leviticus 17:
10 And whatsoever man there be of the house of Israel, or of the strangers that sojourn among you, that eateth any manner of blood; I will even set my against that soul that eateth , and will cut him off from among his people.
11 For the (Hebr. nephesh) of the is in the blood (Hebr. dam): and I have given it to you upon the altar to make an atonement for your souls (Hebr. nephesh): for it is the (Hebr. dam) that maketh an for the soul (Hebr. nephesh).
12 Therefore I said unto the children of Israel, No soul (Hebr. nephesh) of you shall eat blood (Hebr. dam), neither shall any stranger that sojourneth among you eat blood (Hebr. dam).
13 And whatsoever man there be of the children of Israel, or of the strangers that sojourn among you, which hunteth and catcheth any beast or fowl that may be eaten; he shall even pour out the blood (Hebr. dam) thereof, and it with dust (Hebr. aphar).
14 For it is the life of all flesh; the blood of it is for the life thereof: therefore I said unto the children of Israel, Ye shall eat the of no manner of flesh: for the life of all flesh is the thereof: whosoever eateth it shall be cut off.
I have written the original Hebrew for some selected words in verses 11-13. The Hebrew word, nephesh, does not have a clear English equivalent and is translated into soul, living being, life, self, person, desire, passion, appetite, emotion. It is the essence of our inner being. I think the idea that nephesh is closely connected to blood is an important part of understanding all the instructions and focus on blood in general in Jewish law.
For instance, as stated in verse 11 above, "it is the blood (where nephesh is found) that maketh an atonement for the soul (nephesh)". When the Israelites sinned, it came from their nephesh, their desire, passion, appetite, ... To make amends, they had to sacrifice it. But instead of sacrificing their own blood (the physical representation of the more abstract nephesh), an animal representing them could be used instead. Their blood would then represent the nephesh where the sin originated and be dashed against all sides of the altar as a sacrifice to God. This would also represent Christ, who like the animals, took our sins upon him and made atonement. There are many approaches to and layers of symbolism related to the ancient practice of animal sacrifice and this is merely one of them. But this relation between nephesh and dam perhaps reflects Jacob's worldview, adding context to his statement in 2 Nephi 9:44
O, my beloved brethren, remember my words. Behold, I take off my garments, and I shake them before you; I pray the God of my salvation that he view me with his eye; wherefore, ye shall know at the last day, when all men shall be judged of their works, that the God of Israel did witness that I your iniquities from my soul (nephesh), and that I stand with brightness before him, and am of your blood (dam).
Jacob didn't write in Hebrew, but I assume that the words translated into "soul" and "dam" here are Nephite equivalents of nephesh and dam. It was important to Jacob that his nephesh was not mingled with and contaminated by the nephesh in the blood of the wicked. Removing his garments marked a separation.
The prohibition to eat blood did not originate in the Law of Moses, though. It was given for the first time in Genesis 9
3 Every moving thing that liveth shall be for you; even as the green herb have I given you all things.
4 flesh with the (nephesh) thereof, which is the (dam) thereof, shall ye not eat.
This is right after the flood when the earth "re-starts" with multiple references back to the creation account. This leads to another verse in Genesis:
And the Lord God of the (Hebr. aphar) of the ground (Hebr. adamah), and breathed into his nostrils the ; and became a living . (Genesis 2:8)
According to instructions in Leviticus 17 and other parts of the Torah, blood should be poured on the ground and covered with dust. It is a reversal of the creation of man who was formed from the dust of the ground and became a living soul. Indeed, "for dust (aphar) thou art and unto dust thou shalt return" (Genesis 3:19). The soul simply returning to the dust from which it was formed does not really sound like the plan of salvation as we know it. But here is the twist:
53 Then Jesus said unto them, Verily, verily, I say unto you, Except ye the flesh of the , and drink his blood, ye have no life in you.
54 Whoso eateth my , and drinketh my , hath eternal life; I will him up at the last day.
55 For my flesh is meat indeed, and my blood is drink indeed.
56 He that eateth my flesh, and drinketh my blood, in me, and I in him. (John 6)
This image may be grotesque enough for a modern reader, but imagine how horrific it sounds to a faithful and strictly Torah-abiding Jew, who would never even think the thought of eating anything with blood in it. When we partake of the blood of other unholy beings, we contaminate ourselves with their impure nephesh instead of becoming holy like God wants us to. But when we partake of the blood of Christ we dwell in him and he in us as stated in verse 56. His nephesh is pure and holy and this is why we can make an exception to the rule. Instead of staying in the dust that we return to at death we are raised up to eternal life at the last day, according to verse 54.
Consider the words of Christ to the Nephites:
And he said unto them: He that eateth this bread eateth of to his soul; and he that drinketh of this wine drinketh of my blood to his soul; and his soul shall never hunger nor thirst, but shall be filled. (3 Nephi 20:8)
The nephesh in the blood of Christ fills up our nephesh and purifies it.