These were to be offered on the altar as a sweet fragrance to the Lord, and were to be offered for atonement so that the people would be accepted by God. The first three (burnt, meat, and peace offerings) were voluntary offerings, and the last two (the sin and trespass offerings) were compulsory offerings.
Each had a prophetic foreshadowing of the sacrifice of Jesus. For example, the burnt offerings were to be “wholly offered.” This foreshadowed Jesus being wholly given to the will of God when he died for our sins. Jesus held nothing back when God laid it upon him to give his life as the offering for our sins. Jesus gave himself fully to God for us.
On the other hand, the sin offering was to be killed at the altar. The inward parts (the fat, including all the fat around the internal organs, the two kidneys and the fat around them near the loins, and the long lobe of the liver) was to be severed from the carcass and offered on the altar as a sweet savor (a pleasing aroma) to the Lord.
Yet, unlike the burnt offering which was “wholly” burnt on the altar, the carcass of the sin offering was to be taken outside the camp and burned in a clean place there. Only the inward parts were burned on the altar.
There is a twofold significance here: First the inward parts of the sin offering were offered on the altar as a sweet savor to the Lord (Leviticus 4:31). This was a foreshadowing Christ who had no sin. Jesus was totally pure from within. Secondly, the author of Hebrews appeals to burning of the carcass of the sin offering in Hebrews 13.
We have an altar, whereof they have no right to eat which serve the tabernacle. For the bodies of those beasts, whose blood is brought into the sanctuary by the high priest for sin, are burned without the camp. Wherefore Jesus also, that he might sanctify the people with his own blood, suffered without the gate. Let us go forth therefore unto him without the camp, bearing his reproach. ~ Hebrews 13:10-13
The word “without” (without the camp, without the gate) in the reference above means outside. Jesus died for the sins of everyone, even those outside of the camp of Israel. The message of the gospel did not stay within the camp, it was carried outside the camp to the whole world.
All the sacrifices which were offered on the brazen altar were to be offered as gifts for a sweet savor to bring God pleasure. This typified Christ in whom God was pleased, and in whom God would accept for us, granting us forgiveness from our sins.
When God commanded Moses to build the Tabernacle, the brazen altar had to be consecrated by the blood of the sin offering before it could be placed into service. It had no power to sanctify without first being the sanctified by the blood of the sin offering.
When the priests were initially consecrated for the service of the priesthood, the brazen altar was also consecrated for service.
Moses killed the sin offering and applied the blood to the horns of the altar to purify it (Exodus 29:12, 36-37; Leviticus 8:15). In scripture, horns are symbolic of power (Habakkuk 3:4). The blood of the sin offering applied to the horns was a type of the blood of Christ: the power of the cross! The cross has power because of the blood Jesus shed.
After the blood was applied to the horns of the brazen altar, Moses poured the remainder of the blood at the bottom of the altar to sanctify it, so that reconciliation could be made upon it.
The blood sanctified the altar making it a most holy altar.
Seven days thou shalt make an atonement for the altar, and sanctify it; and it shall be an altar most holy: whatsoever toucheth the altar shall be holy. ~ Exodus 29:37
Most holy is the same language used to describe the inner most part of the tabernacle where the glory of God rested on the mercy seat.
When Jesus died on the cross, the cross was set apart as most holy to God for every man, for it was there that Jesus died as a sacrifice to redeem us with his precious blood, and because of his blood, the cross has the power to make us holy in the sight of God.