Now there was a man of the Pharisees named Nicodemus, a ruler of the Jews. 2 This man came to Jesus by night and said to him, “Rabbi, we know that you are a teacher come from God, for no one can do these signs that you do unless God is with him.” 3 Jesus answered him, “Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God.” 4 Nicodemus said to him, “How can a man be born when he is old? Can he enter a second time into his mother's womb and be born?” 5 Jesus answered, “Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. 6 That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. 7 Do not marvel that I said to you, ‘You must be born again.’ 8 The wind blows where it wishes, and you hear its sound, but you do not know where it comes from or where it goes. So it is with everyone who is born of the Spirit.”
9 Nicodemus said to him, “How can these things be?” 10 Jesus answered him, “Are you the teacher of Israel and yet you do not understand these things? 11 Truly, truly, I say to you, we speak of what we know, and bear witness to what we have seen, but you do not receive our testimony. 12 If I have told you earthly things and you do not believe, how can you believe if I tell you heavenly things? 13 No one has ascended into heaven except he who descended from heaven, the Son of Man. 14 And as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, 15 that whoever believes in him may have eternal life.
1 Peter 1:3-5
3 Blessed be the God and Father of our Lord Jesus Christ! According to his great mercy, he has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, 4 to an inheritance that is imperishable, undefiled, and unfading, kept in heaven for you, 5 who by God's power are being guarded through faith for a salvation ready to be revealed in the last time.
1 Peter 1:22-23
22 Having purified your souls by your obedience to the truth for a sincere brotherly love, love one another earnestly from a pure heart, 23 since you have been born again, not of perishable seed but of imperishable, through the living and abiding word of God;
From these texts, and their given contexts, we can determine a few things about the "new birth" or about being "born again."
First, it is required. It is essential. I do not mean it is required as in, "If you don't get 'born again' God won't let you in." I mean there is a connection between being born again and our ability to even see the Kingdom of God. John 3:3 says that unless one is born again he cannot see the kingdom of God. Modern English can prove confusing on this point, since many of us as children still asked, "Can I go to the bathroom?" What we really meant was, "May I go to the bathroom?" We were asking for permission. Can or cannot refers to ability, not permission. Jesus is here talking about ability. Unless a man is born again, he is not able to see the kingdom of God. He is blind to it. It is the Greek word dunatai, which means "able". It is the same Greek word used in a similar statement, which I believe is talking about the same thing, in John 6:44, where Jesus said, "No man is able [dunatai] to come to me unless the Father draws him..."
So, when Jesus says that you must be born again, what He means is that this "being born again" thing must happen to you in order for you to have the ability to see, come to Jesus, etc. It therefore precedes "seeing" and, if I am right about the connection to John 6:44, "coming" (which in the context is obviously figurative for "believing").
Second, it is something that happens to you. I try not to spend too much time pointing out the obvious, but the phrase is "born again", not "choose anew" or something like that. Birth is something that happens to you. It is the act which is required to happen to you in order for you to live your new life in the world. Peter is explicit in 1 Peter 1:3 in stating that God caused it to happen for us. When one is born, one is not a cooperative party, involved in partnership. One is helpless. Birth is the beginning of your new life and the unfolding of your nature.
Third, it is normative for Christians. Peter assumes the readers, as Christians, are all included in it. He says how God has "caused us..." to be born again, for example. Combined with the previous two observations, which are from the texts in John, you can see that this is a normative fact for Christians, not some optional or subsequent future experience. If you aren't born again, you aren't a Christian. If you are born again, there is something new alive inside of you, out of which you are able to "see" and "come" to Jesus.
Fourth, it happens by the Spirit. Jesus calls being born again being "born of the Spirit." The Holy Spirit is somehow at work to bring about the new birth. This is yet another reason why I believe John 6, one of my favorite chapters in the New Testament, is talking about the new birth, among other things.
60 When many of his disciples heard it, they said, “This is a hard saying; who can listen to it?” 61 But Jesus, knowing in himself that his disciples were grumbling about this, said to them, “Do you take offense at this? 62 Then what if you were to see the Son of Man ascending to where he was before? 63 It is the Spirit who gives life; the flesh is no help at all. The words that I have spoken to you are spirit and life. 64 But there are some of you who do not believe.” (For Jesus knew from the beginning who those were who did not believe, and who it was who would betray him.) 65 And he said, “This is why I told you that no one can come to me unless it is granted him by the Father.” (John 6:60-65)
This small section essentially ties up the conversation Jesus has been having about Him being the "bread of life", the unbelief of his hearers, and how such belief is the result of God's action, of God granting it, of the Father drawing and opening eyes. In other words, Jesus is essentially explaining to their face why they don't get it ("This is why I told you..."). They are blind. The Spirit has not given them life.
Fifth, it happens through the Word of God. This, I believe, connects to Romans 10 where Paul says that "faith comes by hearing... hearing the Word about Christ." The means or instrument which God uses, by the Spirit, to cause us to be born again is the Word of God or more specifically the truth of the Gospel. This is why, if my understanding is correct, Luther said that the new birth is faith. I'm not sure I agree completely, but Luther picks up on the strong connection between the two. If they are not the same thing, one awakens the other. The lights go on. Your eyes have been opened. You take your first breath as a new creature with new sight and new lungs.
Further comments: I believe the "bread of life" discussion in John 6 sheds amazing light on the dynamics of this event, of who is at work in it, and of what humanity looks like in the absence of this divine work. There are various verbs Jesus ascribes to the Father in this section of Scripture in regards to His activity toward people, and I believe, given the context, that Jesus is referring to the same thing with all of them. The Father gives people to the Son (v. 37, 39), the Father draws people (v. 44, and the Father grants something to people (v. 65). But the giving, drawing, granting is effectual. It seems clear to me, especially in verses such as verse 37 where it says "all that the Father gives to me will come to me", that this activity of the Father, by the Spirit, yields people "coming" to Jesus to embrace and eat of Him as the Bread of life. Belief results, every time, from this activity of the Father. This does not mean that God does the believing for us. It means, I believe, that believing, coming, eating, or however you want to say it, is the natural activity of a person whom the Father has given to the Son. I believe this is the same thing spoken of in the verses about new birth. God opens our eyes, grants us a new spiritual life within us, through hearing the Word, applied by the Holy Spirit, and the natural results -like breathing- is to see and believe in and eat of Jesus.
Not that experience is the litmus test of truth, but this conforms to my experience. There was a time when suddenly the lights went on, where I saw that my delusion of "goodness" was just that, and where I saw that Jesus did everything I needed on my behalf and was who I needed. I did not choose to have that change of heart, that new perspective. It fell upon me through someone telling me about the cross of Christ.