The law in question actually reads, "You shall abstain from eating the limb of a living animal". This law may seem peculiar at first. How could such a law take it's place beside such monumental laws as Murder and Theft? Secondly, who on earth would consider eating something that was still alive? Granted, there are some cultures in the Far East and Africa who do just that, but for the majority of the world, this doesn't seem like much of a problem. This law is, however, the epitomy of what the Seven Laws stand for. This law stands to show us that just meeting the letter of the law is not enough. In order to be considered one of the "Righteous of the Nations", one should strive to go beyond merely what is required and attempt to attain a pious lifestyle. In this law in particular, beyond simply abstaining from eating limbs from living animals, it teaches us to respect all creatures as creations of the Living G-d. Abstaining from cruelty to animals shows respect to the spark of G-d that exists within everything within creation.
 
    This law is explicit in the text of the Bible. In Genesis 9:3-5, G-d commands Noah, saying, "Every moving thing that lives shall be food for you. I have given you all things, even as the green herbs. But you shall not eat flesh with its life, that is, its blood. Surely for your lifeblood I will demand a reckoning; from the hand of every beast I will  demand it, and from the hand of man." Most think that this refers to eating meat raw, or even eating it medium rare, but this is not the way that it is interpreted. This refers to the fact that an animals soul is tied closely in some way to its blood, and when it dies, this animals soul departs from the blood. In order to show respect to the animal and to G-d's commandment, one should drain any excess blood from the animal when the animal is slaughtered, and before cooking. So long as this vitalizing soul exists within the animal, the animal is forbidden as food.