1 Corinthians 6:11 (ESV)

11 And such were some of you. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God.

Paul reminds the Corinthians that some of them were indeed such (this word expresses his disgust at the sins mentioned in 1 Corinthians 6:9–10). But with their conversion, they were washed (literally, washed off), sanctified, and justified.

The word washed refers directly to baptism, the ceremony that signifies a person’s cleansing from sin. A person who is cleansed from sin is at the same time sanctified (set apart in Christ and by the Spirit) and justified (declared just in the eyes of God).

All three these events—washing, sanctification, and justification—take place in the name of the Lord Jesus Christ and by the Spirit of God. This phrase, too, probably points to the ceremony of baptism (see Matthew 28:19).

By reminding them of their baptism, Paul is reminding the Corinthians of the radical change that has been effected in their lives through their unity with Christ.