Understanding Sacrifices 
While animal sacrifice (“korbanot;” “zevachim;” etc.) is not practiced in Judaism at this time, much of Jewish observance is derived from it. Less directly, this is true of Christianity and Islam, too. Many terms and acts have their basis in the sacrificial practices described in Torah. For that reason, I advocate understanding the sacrifices, even by those who would never consider doing them. This piece, taken from the introduction to the Soncino edition of the Talmudic tractate “Kodashim” — which deals with matters pertaining to sacrifices — is one good place to start.
The origin of sacrifices is wrapped in obscurity. Many widely differing theories have been propounded in explanation, but all are highly conjectural. All that can be said with certainty is that sacrifices are found to have formed a universal element of worship from the earliest times, and that there are traces among the precursors of Israel of sacrificial practices anterior to those instituted in the Torah. This admission does not detract from the claim of the sacrificial laws of the Torah to divine origin, any more than the fact that religious belief did not begin with the Sinaitic Revelation affects the validity of the Religion of Israel. On the contrary, the universality and antiquity of sacrifices only serve to testify to a deep-rooted sacrificial instinct in the human heart which seeks to respond to the claims of God upon man, and which like all other instincts needs correcting, purifying and directing.
The need for a reconciliation of man with the higher power on whom his welfare depends lies after all at the heart of all religion. Religious consciousness has been defined by William James as consisting in a sense (a) of uneasiness ‘that there is something wrong about us as we naturally stand’, and (b) of a solution for that uneasiness — of a sense ‘that we are saved from the wrongness by making proper connection with the higher powers’. In mythology and polytheism the gods are filled with envy, anger and hatred, and sacrifices are brought in order to effect a reconciliation and re-establish connection with them. But the God of Israel can be angry only on account of injustice, and cannot be reconciled otherwise than by the doing justly, loving mercy, and walking humbly with Him. It was therefore essential to transform the crude ideas and desires concerning man’s approach to God by filling them with a spiritual ethical content; and it was for securing this end that the sacrifices instituted in the Torah were designed as a most effective means.
How were the sacrifices prescribed in the Torah to serve this purpose? In considering the Jewish sacrificial system, we are impressed by two unique features which characterize it. First, sacrifices were ordained exclusively for ritual or religious sins, and not for social sins.  Second, no sacrifice could be offered in expiation of the deliberate transgressions but only for such offences as had been committed in error or under constraint. These two reservations, which have no parallel in other sacrificial systems, affect the whole quality of the sacrifices of the Torah. Not the needs of God are the sacrifices intended to satisfy, but the needs of man. They are no longer conceived as gifts to an offended Deity in appeasement of its anger, or in reparation for a wrong done to fellowman. Their aim is essentially man’s spiritual regeneration and perfection. They are designed, in all their parts, to foster in the mind of the worshipper a sense of the awfulness of ritual sin, in that it creates an estrangement alike between man and God and between man and man.
 http://www.come-and-hear.com/talmud/kodashim.html (posted online from the introduction to the Soncino edition of tractate Kodashim.)
 The guilt-offering [“Chatat”] entailed by the social offences enumerated in Lev. V, 21ff, was required only if the offender had denied his guilt on oath, his offering being in expiation of his sin against God rather than his fellow. As for the sin he had committed against his fellow, ‘even if he were to bring all the “rams of Nebaioth” (Isaiah, 60:7) in the world, he would not be forgiven until he obtains pardon from his fellow’ (B.K. 92a); see also Yoma 856 [this might be a misprint, originally meant as 85b].