The Holy Spirit is the Third Person of the Godhead (i.e. Third Person of the Trinity). The Holy Spirit’s primary goal in our lives is to point us to Jesus (John 15:26). The Holy Spirit is kind of like a spotlight that directs our attention to the “main actor” of salvation history who is Christ Jesus. (It’s His work that has saved us, after all.) In John 16:4-15 Jesus, if you will, gives us the Holy Spirit’s “job description.”
First, it is the work of the Holy Spirit to convict (or convince) the world concerning sin - that we have not merely made mistakes in life but that we are, in fact, sinners in rebellion against God who have earned the just penalty of eternal death. (The wages of sin is death . . . Romans 3:28). It takes the work of the Spirit on us to convince us we are, in fact, in this most dreadful state, for apart from the Holy Spirit, we will not see just how fallen our condition truly is. Without the Holy Spirit we will constantly defend our actions; we will constantly try to justify ourselves.
Second, only the Holy Spirit can open eyes to see that righteousness is not to be found in what we do or don’t do. Righteousness is found only in this: that through Jesus’ suffering, death, resurrection and ascension, He goes to the Father on behalf of the whole human race and stands before His Father as the only truly Righteous One, so that everyone whose died in the waters of Baptesm and has had their lives buried in Him, are seen by the Father as righteous with a righteousness not their own, but rather a righteousness that belongs to Christ.
The third work of the Holy Spirit is to convict (or convince) us that God’s wrath at our sin cannot harm anyone whose been tucked into Christ by Baptism. (Satan would like to convince you otherwise.) Jesus has weathered the storm of the Father’s wrath for us on the cross. So, when the ruler of this world, Satan, whose very name means the accuser, comes to charge you and me in the courtroom of heaven at the Judgment Seat of God and demand our life-blood as his own, his case against us is thrown out of court - because the penalty for our sin has already been paid by Jesus. And so the ruler of this world is judged - judged as having no claim anymore upon you. He has no case.