In Leviticus there are four substances that act as "detergents," to use Jacob Migrom's evocative description.
The four detergents used in ritual purification are fire, blood, oil, and water. Each detergent seems to have a domain of associations:
Fire -- Associated with God. Think: Moses and the burning bush, the pillar of fire leading Israel through the desert, the blazing theophany upon Mt. Sinai.
Blood -- The primary ritual detergent, associated with the animal world. The blood is the "life force" of animals, human and non-human.
Oil -- Associated with the land, the domain of agriculture and the human sphere of work. Accordingly, oil is used mainly in the social and political sphere, as with the anointing of a king.
Water -- With oil associated with the land, water completes the picture and functions as a multi-use detergent, from everyday to ritual purifications.
As mentioned above, blood is the primary ritual detergent, especially for the expiation of sin. Why was this the case? Because blood is "life":
For the life of a creature is in the blood. (Lev. 17.11a)
This notion sits at the heart of the Levitical prohibition concerning consuming blood. No human being has a right to the life of an animal. The meat of an animal may be eaten, but the life of the animal must be returned to God. Life is sacrosanct and is under the purview and jurisdiction of the Deity.
This explains why blood, as life itself, is the ritual detergent par excellence. The basic idea at work in Leviticus is that sin accumulates in the community, like a pollution that adheres to everything. Think of an oil spill. Or the soot that covered everything in London in a Dickens' novel. The ritual and moral impurities in Israel built up in a similar way. Blood was the main detergent used to clean the community and the sacred space of these impurities. Blood had this power because the impurities marked the encroachment of death. And only life could wipe death away.
That idea, life wiping away death, is the critical insight.
Here's why. In many sectors of Christianity, the atoning blood of Jesus has become associated with the appeasement of a wrathful God. But that's not what you see in Leviticus. God doesn't demand blood and blood is not offered to God to appease God's wrath. In contrast to the pagan gods, Israel's God pointedly didn't eat animal meat or drink blood. Blood was, rather, simply used as a detergent.
Trouble was, animal blood was only a temporary detergent, so the cleansing had to be repeated over and over and over again. Thus, according to the book of Hebrews, what sinful humanity needed was a detergent so strong it could be offered "once for all." This was the blood of Christ, God's very own life, his own blood, that could wipe away every trace of sin and death. Note, there is no wrathful God here. Simply the graceful provision of the most potent detergent--God's own life--that could, in a single act of purification, wipe away every sin, of every person, for all time.