In "The Gift", we get this exchange:
XANDER
Why blood? Why is it Dawn's blood,
why couldn't it be, like, a lymph ritual?
SPIKE
'Cause it's always gotta be blood.
XANDER
We're not actually discussing dinner
right now.
SPIKE
Blood is life, lackbrain. Why do you think
we eat it? It's what keeps you going, makes
you warm, makes you hard, makes you
other than dead. 'Course it's her blood.
This goes back to Biblical sources where the Hebrew priests sacrificed animals on the altar and sprinkled the blood on it and where Moses sprinkled the blood of the covenant on the people (Ex 24:8). In Leviticus 17:11, the explanation for kosher killing is stated as "For the life of the animal is in the blood, and I have given it to you to make atonement for yourselves on the altar; it is the blood that makes atonement for one's life." There is no medical reason blood would be credited with consciousness or life, but lack of blood certainly ends life. In our own culture, life is considered to be in the brain and people may be disconnected from medical apparatus when they are brain-dead. This may change somewhat in the future as changes in personality are noted with organ transplant recipients. There are classic stories of someone getting a heart transplant and suddenly wanting to buy a motorcycle and a bit of research shows the organ came from a motorcyclist.
Blood has always been the religious symbol of life regardless of whether you worship God or Satan.