Animal sacrifice is indeed a very old cross-cultural practice. The general idea is that the sacrificed animal is offered to a deity as literal sustenance for them or at least as a gift to gain favor with the deity. The Greeks, for example, would often eat much of the sacrificed animal but burn the rest as an offering the gods. In Leviticus you frequently see the phrase “fragrant odor to the Lord” in reference to an animal burned in sacrifice; this is a remnant of a very old practice in which the smell of burning animal flesh was said to appease a deity and gain favor with it. (Also in Leviticus, fat and blood are not to be consumed; the fat is reserved to be burned as an offering to God and the blood, being the very life itself, was also reserved for God alone). In the Old Testament view, sacrifices went beyond gaining favor with the deity to having a role of purification and atonement (blood was seen as having a purifying effect, shedding of blood is necessary to pay for sins); the blood sacrifices thus atoned for transgressions and purified the Tabernacle where God was said to dwell. Jesus’ sacrifice extends the concept further: his sacrifice was necessary to atone for all our sins. There is some explanation of the rationale behind Jesus’ sacrifice in the Pauline epistles:
“Since we have now been justified by his blood, how much more shall we be saved from God’s wrath through him! For if, while we were God’s enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life!” Romans 5:9–10
It’s not so much that Jesus was sacrificed to, but sacrificed for. His death as the ultimate sacrifice atoned for the sins of humanity.