Numbers chapter 8 tells us that the Levites were separated from the children of Israel for God ( verse 14) to do the work in the tabernacle on behalf of the children of Israel ( verse 19). They were to make atonement for the children of Israel ( verse 19). To make atonement means to right a wrong done, or to make amends. Biblically it means to remove the guilt of man.
The Levites made atonement for the children of Israel not by offering sacrifices, that was the job of the priests, but by being offered themselves to ” perform the work of the Lord” ( verse 11) i.e to perform all the duties and responsibilities they were given related to the tabernacle.
By performing their role correctly they would keep the children of Israel from sinning, from touching what they should not touch or doing what they should not do. In that sense they made atonement for the children of Israel, they kept the children of Israel from guilt.
God wants us to make atonement for one another just as the Levites made atonement for the children of Israel. He wants us to consecrate ourselves to Him and live as He has called us to live, and through our influence keep one another from sin.
This responsibility we all have to one another is spelled out in James 5:19-20
19 Brethren, if anyone among you wanders from the truth, and someone turns him back, 20 let him know that he who turns a sinner from the error of his way will save a soul[a] from death and cover a multitude of sins.
The most effective way to turn a sinner from the error of his way, is by our example. If we do what the Levites did, consecrate ourselves to God and live the life He has called us to live, our example will turn a sinner from the error of his ways. We will keep each other from the guilt of sin, making atonement for one another.