Did the ancient Hebrews believe that blood had unique spiritual properties? I seem to recall learning at some point during an Old Testament study that they did, and that the belief explained things like the significance of the blood that was part of the animal offerings required in the Pentateuch.

We're trying, in this question, to track down the significance behind an apparent New Testament dietary prohibition against the consumption of animal blood, as given in Acts 15:10.
Such a belief is clearly expressed in both Genesis and Leviticus.


  Genesis 9:4
  
  But flesh with the life thereof, which is the blood thereof, shall ye
  not eat.
  
  Leviticus 17:11-14
  
  11 For the life of the flesh is in the blood: and I have given it to
  you upon the altar to make an atonement for your souls: for it is the
  blood that maketh an atonement for the soul.
  
  12 Therefore I said unto the children of Israel, No soul of you shall
  eat blood, neither shall any stranger that sojourneth among you eat
  blood.
  
  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 thereof,
  and cover it with dust.
  
  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 blood of no manner of flesh: for the life of all flesh is the
  blood thereof: whosoever eateth it shall be cut off.


In both cases, the blood-as-life theory is used specifically as the reason why eating blood should be forbidden.