The purposes of sacrifice are: to give honor or adoration to God, to offer Him thanks, to beg a favor, or to make propitiation.
In other words, the purposes of sacrifice are: adoration, thanksgiving, petition, and atonement. It is natural for man to give outward expression to the feelings that move his interior being. For this reason he bursts out in praise when he thinks of the greatness and holiness of God; he must give something up as a sign of gratitude; he must offer a gift when he feels his insignificance in begging a favor; and he tries all kinds of penitential works when he realizes his iniquities.