Jesus gave specific instructions when he launched the church that included the ceremony of baptism:
 Matthew 28 18 
Jesus came and told his disciples, “I have been given all authority in heaven and on earth. 19 Therefore, go and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit. 20 Teach these new disciples to obey all the commands I have given you. And be sure of this: I am with you always, even to the end of the age.” 
The Apostles followed these instructions. Acts 2 shows the result.---
Acts 2:36So let everyone in Israel know for certain that God has made this Jesus, whom you crucified, to be both Lord and Messiah!”37 Peter’s words pierced their hearts, and they said to him and to the other apostles, “Brothers, what should we do?”38 Peter replied, “Each of you must repent of your sins and turn to God, and be baptized in the name of Jesus Christ for the forgiveness of your sins. Then you will receive the gift of the Holy Spirit. 39 This promise is to you, and to your children, and even to the Gentiles—all who have been called by the Lord our God.” 40 Then Peter continued preaching for a long time, strongly urging all his listeners, “Save yourselves from this crooked generation!” 

41 Those who believed what Peter said were baptized and added to the church that day—about 3,000 in all.
We see the following in this passage:
1. Baptism is a necessary action following belief in Jesus. It is a step of faith and an act of obedience to your creator.
2. Baptism is a formal entrance ceremony to the church after you have acknowledged the basic beliefs of the faith.
Belief Defined: In the Acts passage above, Peter tells the crowd that they must repent of their sins and turn to God. We need to answer the question then, “What does it mean to repent of your sins and turn to God?”
I Peter chapter 1 says,
18 For you know that God paid a ransom to save you from the empty life you inherited from your ancestors. And it was not paid with mere gold or silver, which lose their value. 19 It was the precious blood of Christ, the sinless, spotless Lamb of God. 20 God chose him as your ransom long before the world began, but now in these last days he has been revealed for your sake.
21 Through Christ you have come to trust in God. And you have placed your faith and hope in God because he raised Christ from the dead and gave him great glory. 22 You were cleansed from your sins when you obeyed the truth, so now you must show sincere love to each other as brothers and sisters. Love each other deeply with all your heart. 23 For you have been born again, but not to a life that will quickly end. Your new life will last forever because it comes from the eternal, living word of God. 24 As the Scriptures say,

“People are like grass;
 their beauty is like a flower in the field.
The grass withers and the flower fades.
 25 But the word of the Lord remains forever.”
And that word is the Good News that was preached to you.
“What does it mean to repent of your sins and turn to God?”
Peter wrote his letter so that we would know that God loves us even though we rebel (sin) against him. All of us would rather be in charge than respectfully follow our creator-God. We are essentially self-centered and we either tell God we don’t want to follow him, or we just tell him to leave us alone. When we rebel against God we end up breaking his law and injure our relationship with Him and others.
The possibility of reconciliation (a new relationship with God) was purchased for us by Jesus. That is the good news (the Gospel). It isn’t something that we could earn, it isn’t something we could buy, the damage that our sin does is too great for that. Jesus, the only sinless man to ever live is the only one who could take our place. He took our punishment, paid for our sins, and he did it out of love for us. When we put our trust in Jesus (instead of our inherent goodness, or our good works), the Word says we have new life. A life that lasts forever. As evidence of that changed heart, our behaviour changes. We now want a relationship with God and we want to follow his ways. This change of heart and direction is called repentance.

The Meaning of Baptism: 
Romans 6: Or have you forgotten that when we were joined with Christ Jesus in baptism, we joined him in his death? 4 For we died and were buried with Christ by baptism. And just as Christ was raised from the dead by the glorious power of the Father, now we also may live new lives.5 Since we have been united with him in his death, we will also be raised to life as he was. 6 We know that our old sinful selves were crucified with Christ so that sin might lose its power in our lives. We are no longer slaves to sin.7 For when we died with Christ we were set free from the power of sin. 8 And since we died with Christ, we know we will also live with him. 9 We are sure of this because Christ was raised from the dead, and he will never die again. Death no longer has any power over him. 10 When he died, he died once to break the power of sin. But now that he lives, he lives for the glory of God. 11 So you also should consider yourselves to be dead to the power of sin and alive to God through Christ Jesus.

Therefore, according to Romans 6 Baptism symbolizes that:
 a. We are united with him in his death.
b. We will be raised to new life.
 c. We are no longer slaves to sin.
d. We have new life, which will be fully realised in heaven.