Blood can symbolize a variety of things. As a spiritual metaphor, blood can mean or be symbolic of Christ. Jesus Christ gave his life for mankind (Simon is considered the Christ figure in this book), and it took the spilling of his blood to kill him. Christians remember him by having communion or drinking a small drink of wine or grape juice as a symbol of Christ's sacrifice.
Blood can also symbolize vengence or a first kill. There are many "firsts" in life that occur because of blood being spilled. A girl's entrance into womanhood or a gangster's first fight or murder are just a couple examples of the entrance to something new. For Jack, the first kill of a pig results in a very vivid image of the spilling of blood.
Then Jack found the throat and the hot blood spouted over his hands. (Chapter 8)
This kill symbolized Jack's entry into the savage world with no room for turning back.
In Simon's experience with the Lord of the Flies (a fight with evil), Simon undergoes a seizure. This leaves him hallucinating and broken. Then this vivid description of his last moments occurs:
Even when the vessel broke in Simon’s nose and the blood gushed out they left him alone, preferring the pig’s high ﬂavor.With the running of the blood Simon’s ﬁt passed into the weariness of sleep. (Chapter 9)
After awaking from this slumber, Simon dies trying to tell the boys the truth about the Beast but they won't hear his message.
The blood symbolizes the shedding of an old life and entry into a new life for both boys.