In John 3.3 Jesus said that no one can see the kingdom of God unless he is born again. In 1Pet.1.3, Peter says God has given us new birth. How does a person know for sure that he is already born again according to what Jesus says?
Jesus Christ said to Nicodemus in John 3:3:
Jesus answered and said to him, “Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God.”
Also, the Lord through Peter said in 1Pet. 1:3
Blessed be the God and Father of our Lord Jesus Christ, who according to His great mercy has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead,
The phrase “caused us to be born again" is referring to the same spiritual new birth that Jesus spoke about in John 3. It is the spiritual renewal caused by the work of the Holy Spirit in the heart of a person so they may become a follower of Jesus Christ and join into the body of Christ, the Church. Being “born again” is also the same as becoming a “new creation” and becoming a “new creature in Christ," as Paul describes it in 2Cor 5:17.
In short, being "born again" means receiving a new spirit through faith in Jesus Christ. All who believe in Jesus Christ as Savior have been born again. This new birth is necessary because until we have been born again, we are by nature opposed to God and unable and unwilling to know Him truly. The sinful nature of man was introduced through the sin of Adam in the Garden of Eden, as told in Genesis 2 and 3. In Genesis 2:16-17 we read:
The LORD God commanded the man, saying, “From any tree of the garden you may eat freely; but from the tree of the knowledge of good and evil you shall not eat, for in the day that you eat from it you will surely die.”
The statement: “you will surely die” means to die spiritually. Due to Adam's sin, they died a spiritual death, which is not the same as dying physically. Physical death came later as the result of God's curse on the Earth and all things in it (see Genesis 3:17). Since Adam, every human ever born has come into the world sharing the same fallen nature inherited from Adam. We are all born spiritually dead (see Romans 3:10-18).
Jesus Christ was not born with the nature of Adam, because He was conceived by the Holy Spirit in Mary's womb, so His nature was not sinful. He was the Word made flesh and dwelt among us. Though he was not under the penalty of death Himself, nevertheless He willingly died in our place to pay the penalty for our sin.
By our faith and trust in that sacrifice, we are given His Spirit and made new again spiritually - we are born again or spiritually reconnected to God. The Apostle John teaches how we might know that someone has truly come to be born again in 1John 2:3-6:
By this we know that we have come to know Him, if we keep His commandments. The one who says, “ I have come to know Him,” and does not keep His commandments, is a liar, and the truth is not in him; but whoever keeps His word, in him the love of God has truly been perfected. By this we know that we are in Him: the one who says he abides in Him ought himself to walk in the same manner as He walked.
John is not suggesting that the evidence of our new birth will be a perfect sinless life, since this is not possible for any man until we receive our new, sinless body at the resurrection of the saints (1Cor 15). Instead, John is explaining that the new birth will be accompanied by new thinking and new living, in conformance with Jesus' word.
If you have doubts as to whether you have understood and believed the Gospel (so as to be born again), please read this article on How to Become a Christian.