The Holy Spirit convicts the world of their sin.
John 16:7-11 (ESV)
7 Nevertheless, I tell you the truth: it is to your advantage that I go away, for if I do not go away, the Helper will not come to you. But if I go, I will send him to you.
8 And when he comes, he will convict the world concerning sin and righteousness and judgment:
9 concerning sin, because they do not believe in me;
10 concerning righteousness, because I go to the Father, and you will see me no longer;
11 concerning judgment, because the ruler of this world is judged.
The Holy Spirit opens our eyes to the deep truths in Scripture.
2 Timothy 3:16-17 (ESV)
16 All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness,
17 that the man of God may be competent, equipped for every good work.
John 14:26 (ESV) But the Helper, the Holy Spirit, whom the Father will send in my name, he will teach you all things and bring to your remembrance all that I have said to you.
1 Corinthians 2:13 (ESV) And we impart this in words not taught by human wisdom but taught by the Spirit, interpreting spiritual truths to those who are spiritual.