Clearly, in the sin offering described here, atonement is used in the sense of "a covering," and therefore as a means of forgiving sin. By contrast, in the burnt offering sin is nowhere seen because it is not part of what the burnt offering teaches. In it, God is satisfied because the offerer has met His requirement through his life, by the righteous way he lives his life. Thus, the offering shows the offerer accepted.
However, not all sense of covering is lost in the use of "atonement" in Leviticus 1. Here, the essence of covering arises in the fact that the offering covers—is fitting or appropriate—in the sense of meeting all conditions. The conditions involve a life of sincere, wholehearted, and loyal devotion to God.
John W. Ritenbaugh
The Offerings of Leviticus (Part Two): The Burnt Offering
The English word atonement appears in Leviticus 4:20, 26, 31, 35 in reference to these sin offerings, as it does in Leviticus 1:4 in reference to the burnt offering: "Then he shall put his hand on the head of the burnt offering, and it will be accepted on his behalf to make atonement for him." This is the last time "atonement" appears in reference to the sweet-savor offerings in Leviticus 1-3.
"Atonement" may mislead some because we almost automatically think of a covering for sin. Atonement for sin normally makes one acceptable before God, but sin is not present in the sweet-savor offerings. Nonetheless, the word indeed conveys the sense of acceptance but on a different basis than in the sin and trespass offerings. The basis for acceptance in the sweet-savor offerings is the offerer's perfect devotion, picturing the devoted, sinless Christ worshipping God.
Concerning the sin and trespass offerings, "atonement" is used in the way we normally understand it: as a covering, payment, expiation, or propitiation made for sin. It is as though the offerer is charged just as the police charge a person with a crime. In this case, though, the offerer is charged with sin, and something must expiate it. The sin and trespass offerings, then, indicate the payment of a legal obligation to an authority, one that meets the legal requirement of that authority. To expiate sin, the payment must be in blood; a life must be given. The Authority is God, as His law has been broken.
The wages of sin is death (Romans 6:23). Whenever a person sins, the law has the power to take that person's life. It has such power over us that, for our debt to be paid, a life is required. Nothing less is suitable to expiate sin. In the symbolism of the sin and trespass offerings, the life of an animal is given, covering the indebtedness and breaking the power the law has over us.
In actual practice, the ritual proceeded like this: The offerer brought his animal before the priest and then laid his hand upon the head of his offering. Symbolically, a transfer took place so that the animal is understood as portraying the sinner making the offering. The animal then died, and the penalty was considered paid.
In Romans 6:2, Paul writes that we are "dead to sin," and in Romans 7:4, that we are "dead to the law." The ritual portrays these truths. The sin and trespass offerings picture a convicted sinner coming before God to receive the judgment of death. However, the animal's death portrays Christ's vicarious death in our stead, for in reality, since He is the offering, our sins have been transferred to Him. In this way, we are atoned for and redeemed.
John W. Ritenbaugh
The Offerings of Leviticus (Part Six): The Sin Offering