Question: What did they do with the sacrifices? Did they just burn them? Did they eat them? What exactly was the purpose of giving a sacrifice? To seek forgiveness? To show worship to God? Or to get prayers answered? Oh, and what’s the deal with incense?
Response: Apart from meat sacrifices, there were also grain (or flour) and oil sacrifices and money was given.
The regulations on a few meat sacrifices required that it be entirely burned, but in most cases only the fatty portions and some organs were burned. The meat was eaten, sometimes by the priests and Levites as their income, and sometimes by the worshipers as part of their worship celebration. (Most people around the world then and now don’t get much meat in their diet except at times like that.) The skins went to tanners, the bones, etc. that weren’t used were discarded. They are biodegradable.
God decreed that without the shedding of blood there was no forgiveness of sins. The animal sacrifices were obviously not permanently effective because they kept doing them over and over again. The shedding of Christ’s blood was permanently effective. It ended the value of ever having another animal sacrifice for the forgiveness of sins.
God decreed incense for Israelites as the sensory symbol of the prayers of His people ascending to His throne of mercy.