"But you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth." Acts 1:8
Jesus promised the coming of the third person of the Trinity, the Holy Spirit, to dwell in the lives of the believers. The Spirit brought amazing change in their lives. He would be God, living and acting in their hearts. No longer would their relationship with God be limited due to location, time, or physical limitations. Now they have unlimited access to God. Jesus knew that this would be necessary for the lives they would live and the ministry that He would give them. They could not live out God's mission for them without the Spirit, so Jesus told them to wait for His coming before they ventured out.
God's mission for them was to take the Gospel - the message that Jesus died as a substitute for our sins, was buried, and raised to conquer sin, death, and hell on our behalf - to all of the earth. Obviously, if this mission depended solely on their abilities, it was doomed to failure. They had been unable to get anything right until now and were surely destined to mess it up again. When the religious authorities came for Jesus, they ran in fear; now they were asked to stand against the same authorities that had killed Jesus. In addition, they would face obstacles at every turn. Without God, they would never succeed.
God had prophecied about the coming of the Spirit in Joel. Jesus had promised His coming multiple times in the Gospels. Now He has ascended to Heaven and the disciples are gathered, praying and seeking the Holy Spirit's coming. On the day of Pentecost, God sends the Spirit. Immediately, we see His presence equipping and enabling the disciples to carry out God's mission for them.
One obstacle before them was the language barrier. In Genesis 11, the people of the earth had united in an attmept to make themselves like God. As a result, He had confused their language and scattered them over the earth. Now, these different languages provide an obstacle for His message of redemption. So the coming of the Spirit enables His followers to proclaim the message of Jesus in the languages of all the people gathered in Jerusalem. This enabled them to hear and respond to God. From there, they were able to go to their homes and preach the Gospel in their language.
In addition, this provided confirmation of God's work and message by fulfilling the prophecy of Joel and the promise of Jesus. The coming of the Holy Spirit is proof of God's presence in their lives. This is especially important when the message goes from the Jews to the Gentiles and serves as confirmation that they can receive the Gospel as well.
We also see that the Spirit convicts of sin and grants faith to those who hear the message. Salvation is God's work, from start to finish; it does not depend on man's power or ingenuity. He is the One who has made provision for our sin. He is also the one who reveals our sin to us and gives us faith to turn to Him. Jesus said that the Spirit would come to ". . . convict the world of guilt in regard to sin and righteousness and judgment: in regard to sin, because men do not believe in me; in regard to righteousness, because I am going to the Father, where you can see me no longer; and in regard to judgment, because the prince of this world now stands condemned" (John 16:8-11). This is the work we see Him doing here as the people hear of their sin, Jesus' provision for it, repent and turn to Him.
The same things hold true for us today. We are called to continue the work that God gave the disciples - to carry the message of Jesus to the world. Just like them, we are incapable of doing it alone; but just like them, we aren't left alone to do it. The Spirit has come to help us. While we may not face the language barrier, He provides the words we are to speak, draws others to Him, and convicts them of their sin. We are His agents to spread the message; He does the work of convicting of sin, drawing people to Him, and granting repentance.
Just like the disciples, God has given us the Spirit. He provides the power we need for life.