Jesus promised that once He had returned to His Father, He would send the Spirit (also referred to as the Helper, Comforter or Advocate) to His disciples.
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 depart, I will send Him to you. (Jn. 16:7 NKJ)
What does He do? The list is long, but below are a few of the works done by the Holy Spirit.
He lives inside us
The prophet Ezekiel told God’s people that one day He would send His Spirit to dwell inside them.
I will put My Spirit within you and cause you to walk in My statutes, and you will keep My judgments and do them. (Ezek. 36:27 NKJ)
True to His word, just 10 days after Jesus went back to His Father, He sent the Holy Spirit to live inside His disciples (Acts chapters 1-2). The Holy Spirit now lives inside every disciple of God.
...the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you and will be in you. (Jn. 14:17 ESV)
19 Or do you not know that your body is a temple of the Holy Spirit within you, whom you have from God? You are not your own, 20 for you were bought with a price. So glorify God in your body. (1 Cor. 6:19-20 ESV)
As His disciples, we have a member of the Trinity living inside us! Why would He live inside us?
He brings about the new birth
Jesus told a Jewish teacher named Nicodemus that we must be “born again” to become part of God’s kingdom (John 3:1-15). One very important thing the Holy Spirit does is to bring about this new birth. During our baptism in water He “regenerates” us, which is another way of saying we have been re-born. He causes us to be born again and while simultaneously washing away our sins and taking up residence inside us.
And Peter said to them, "Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. (Acts 2:38 ESV)
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. (1 Cor. 6:11 ESV)
5 …He saved us through the washing of rebirth and renewal by the Holy Spirit, 6 whom he poured out on us generously through Jesus Christ our Savior, (Tit. 3:5-6 NIV)
He represents a down payment
In ancient times, a wax seal bearing the imprint of a signet ring was placed upon documents to prove ownership or authenticity. The Bible says that the indwelling of the Spirit seals us proving that belong to God.
13 And you also were included in Christ when you heard the message of truth, the gospel of your salvation. When you believed, you were marked in him with a seal, the promised Holy Spirit, 14 who is a deposit guaranteeing our inheritance until the redemption of those who are God's possession-- to the praise of his glory. (Eph. 1:13-14 NIV)
He is a “deposit” or “down payment” on the inheritance that God has promised us - eternal life with Him.
He helps us want what God wants
The Spirit works to transforming our minds (Rom 12:2) gently shaping our character so that we slowly become more and more like Jesus. This is a process known as “sanctification”. The word sanctify means to set apart for a special work or purpose. We are set apart (sanctified) to do the work of God (Eph 2:10).
Yes, it is God who is working in you. He helps you want to do what pleases him, and he gives you the power to do it. (Phil 2:13 ERV)
16 So I say, walk by the Spirit, and you will not gratify the desires of the flesh. 17 For the flesh desires what is contrary to the Spirit, and the Spirit what is contrary to the flesh. They are in conflict with each other, so that you are not to do whatever you want. 18 But if you are led by the Spirit, you are not under the law. (Gal. 5:16-18 NIV)
The Spirit works against any natural desires that we have which may be wrong. He helps us want to do what is right and gives us the ability to good things.
And much more…
The Holy Spirit also aids us when we pray (Rom 8:26), produces spiritual fruit in us (Gal 5:22-23), distributes spiritual gifts for the good of the church (1 Cor 12:4-11), helps us to understand the revelation of God (1 Cor 2:10-13), and on and on.
The Spirit does all this, and more, without violating our own free will or personal choice. How He does this is a mystery that probably transcends human understanding. As Jesus explained to Nicodemus (John 3:8), we may observe the effects of the Spirit, but not understand how He does it.