i think this phrase is most often used in error - there is no 'conviction' without judgment, and for a reborn believer who looks to Jesus as their substitute, there is no judgment from God.
(Joh 16:7) Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.
(Joh 16:8) And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:
(Joh 16:9) Of sin, because they believe not on me;
(Joh 16:10) Of righteousness, because I go to my Father, and ye see me no more;
(Joh 16:11) Of judgment, because the prince of this world is judged.
the Holy Spirit reproves or corrects the lost person of not believing in Jesus' atonement as the way to approach God. He corrects the reborn believer that they are righteous in God's eyes because of their substitute, Jesus, not based on their own performance. He corrects everyone that it is the devil that has been judged.
the devil is the accuser; he is the one that points out your faults in order to get you into condemnation and stop your faith in God's goodness toward you.
God's correction is accomplished through His word, as His word is given for instruction. He doesn't say 'stop that sinning', He says 'follow My leading through fellowship with Me'; to the extent that we are led by God, we will not sin.