As Ben Witherington says: Most religions in the Greco-Roman world, like most religions in the Ancient Near East had three things in common---- temples, priests, and sacrifices. The death of Jesus was interpreted by the early Christians in terms of many of the common concepts associated with the understanding of sacrifice in the ancient world (see this prior post).
I have been doing some reading on the subject of sacrifices in ancient religions and it has been very enlightening. One of the books that I have found especially helpful was written by W. Robertson Smith (1846-1894). He has some excellent insights into the nature of religious sacrifice in his book, Lectures on the Religion of the Semites (1889).
One of the insights is that in ancient times, a public execution was often seen as propitiatory and in some sense, substitutionary. For example, the case of Achan in Joshua 7. He and his family were publicly executed and then in 7:26 it says: "the Lord turned from his fierce anger". God was angry with the whole nation and the nation suffered a defeat at Ai because of Achan's sin. When Achan was executed, God's wrath was propitiated and the nation was no longer under his wrath.
Smith explains the concept:
Hence, when a tribesman is executed for an impious offence, he dies on behalf of the community, to restore normal relations between them and their god; so that the analogy with sacrifice is very close in purpose as well as in form. And so the cases in which the anger of the god can be traced to the crime of a particular individual, and atoned for by his death, are very naturally seized upon to explain the cases in which the sin of the community cannot be thus individualised, but where, nevertheless, according to ancient custom, reconciliation is sought through the sacrifice of a theanthropic victim. The old explanation, that the life of the sacrosanct animal is used to retie the life-bond between the god and his worshippers, fell out of date when the kinship of races of men with animal kinds was forgotten. A new explanation had to be sought; and none lay nearer than that the sin of the community was concentrated on the victim, and that its death was accepted as a sacrifice to divine justice. This explanation was natural, and appears to have been widely adopted, though it hardly became a formal dogma, for ancient religion had no official dogmas, but contented itself with continuing to practise antique rites, and letting everyone interpret them as he would (pp. 421-22).
It seems that a sacrifice and an execution were not totally dissimilar in the mind of the ancient Semite. Both served to propitiate the anger of the god(s).
Another insight from Smith is that the sacrifices were seen as purging away guilt. He writes:
Another interpretation of piacular sacrifice, which has great prominence in antiquity, is that it purges away guilt. The cleansing effect of piacula is mainly associated with the application to the persons of the worshippers of sacrificial blood or ashes, or of holy water and other things of sacred virtue, including holy herbs and even the fragrant smoke of incense.. . Purifications, therefore, are performed by the use of any of the physical means that re-establish normal relations with the deity and the congregation of his worshippers—in short, by contact with something that contains and can impart a divine virtue. For ordinary purposes the use of living water may suffice, for, as we know, there is a sacred principle in such water. But the most powerful cleansing media are necessarily derived from the body and blood of sacrosanct victims, and the forms of purification embrace such rites as the sprinkling of sacrificial blood or ashes on the person, anointing with holy unguents, or fumigation with the smoke of incense, which from early times was a favourite accessory to sacrifices(p. 426).
It is interesting that water, especially living or running water was seen as able to cleanse (compare the Christian concept of baptism) but a better agent to cleanse away sin was the blood of the victim (compare 1 John 1:7).
Another lesser known practice was for the skin of the victim to be removed and placed over the offerer. This is seen in Genesis 3:21 when God clothes Adam and Eve with coats of skin, it is seen as well as in many other primitive societies. Smith explains:
But when the fresh skin of the victim is applied to the worshipper in the sacrifice, the idea is rather an imparting to him of the sacred virtue of its life. Thus in piacular and cathartic rites the skin of the sacrifice is used in a way quite similar to the use of the blood, but dramatically more expressive of the identification of the worshipper's life with that of the victim. In Greek piacula the man on whose behalf the sacrifice was performed simply put his foot on the skin; at Hierapolis the pilgrim put the head and feet over his own head while he knelt on the skin; in certain late Syrian rites a boy is initiated by a sacrifice in which his feet are clothed in slippers made of the skin of the sacrifice. These rites do not appear to have suggested any idea, as to the meaning of piacular sacrifice, different from those that have already come before us; but as the skin of a sacrifice is the oldest form of a sacred garment, appropriate to the performance of holy functions, the figure of a "robe of righteousness," which is found both in the Old Testament and in the New, and still supplies one of the commonest theological metaphors, may be ultimately traced back to this source (pp. 438-39).
Smith concludes his book with the following:
On the whole it is apparent, from the somewhat tedious discussion which I have now brought to a close, that the various aspects in which atoning rites presented themselves to ancient worshippers have supplied a variety of religious images which passed into Christianity [emphasis mine], and still have currency. Redemption, substitution, purification, atoning blood, the garment of righteousness, are all terms which in some sense go back to antique ritual. But in ancient religion all these terms are very vaguely defined; they indicate impressions produced on the mind of the worshipper by features of the ritual, rather than formulated ethico-dogmatical ideas; and the attempt to find in them anything as precise and definite as the notions attached to the same words by Christian theologians is altogether illegitimate. The one point that comes out clear and strong is that the fundamental idea of ancient sacrifice is sacramental communion, and that all atoning rites are ultimately to be regarded as owing their efficacy to a communication of divine life to the worshippers, and to the establishment or confirmation of a living bond between them and their god. In primitive ritual this conception is grasped in a merely physical and mechanical shape, as indeed, in primitive life, all spiritual and ethical ideas are still wrapped up in the husk of a material embodiment. To free the spiritual truth from the husk was the great task that lay before the ancient religions, if they were to maintain the right to continue to rule the minds of men. That some progress in this direction was made, especially in Israel, appears from our examination. But on the whole it is manifest that none of the ritual systems of antiquity was able by mere natural development to shake itself free from the congenital defect inherent in every attempt to embody spiritual truth in material forms. A ritual system must always remain materialistic, even if its materialism is disguised under the cloak of mysticism (pp. 439-40).