Q: Is there any born again concept ( to get the eternal life ) in Vedas ( Hinduism ) as it mentioned in the Bible?
A: Your question is an example of how both Hinduism and Christ have the same words with some overlap and yet differences. Both Christians and Hindus claim to be born again. The meaning of what it is to be born again and the extent that this goes to is different.
In Hinduism, mainly developed in the Upanishads, to be born again is a necessity and happens to all beings. How a person will be born again is determined by their karma—either upwards or downwards in the cycles of births. The Prashna Upanishad explains, “At the time of death, through the subtle track that runs upward through the spinal channel, Udana, the fifth force, leads the selfless up the long ladder of evolution, and the selfish down. But those who are both Selfless and selfish come back to this earth.” (Question Three, 7). In fact, Hinduism teaches that people are actually not born again, rather they are born again-- and again-- and again… The Aitereya Upanishad mentions not only born again- a second time, but a third time: “It becomes a child in the woman. This is the first birth…the child is their atman, their very Self, and continues their line without break as the second birth. He discharges all their holy duties and shed his body, too, when it grows old, to be born again. This is the third birth.” (Part II, 1-4). One guru (Sri Chinmoy) estimates that everyone passes through all 8.4 millions species before becoming human and then through hundreds or thousands of human births before escaping samsara (the cycle of rebirths) to moksha. In Hinduism, born again refers to the necessary and continual process of reincarnation through the demand of karma. It is not an optional issue of belief or a choice. It is only a question of what kind of existence you will have when you are born again and again.
For Christians the meaning of “born again” comes from a discussion of Jesus with a learned Jewish man named Nicodemus. This is reported in the Bible in the book of John, chapter three. Nicodemus is confused when Jesus says, “No one can see the kingdom of God unless he is born again.” Nicodemus asks Jesus what he means by this, saying, “How can a man be born when he is old?” Jesus explains by making three statements (John 3:3-9). The first is, “Unless one is born of water and the Spirit, one cannot enter the kingdom of God.” By this Jesus is saying that one must not only be born from the waters of his mother’s womb, but there is a need to be born and have life by the Spirit of God. The second statement says, “That which is born of flesh is flesh, and that which is born of the Spirit is spirit.” This is a further explanation of the same thing. You can live an earthly and fleshly existence, but there is a spiritual kingdom into which men must also be born to have eternal life. The third statement is, “The wind blows where it wishes and you hear the sound of it, but do not know where it comes from and where it is going; so it is with everyone born of the Spirit.” The second birth Jesus refers to is produced by the Spirit of God. You can tell something has happened to a person, but you cannot see the event itself as you might in the first birth. A famous verse in the Bible is connected with this—John 3:16. “For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish, but have everlasting life.” The means for this second birth—or getting everlasting life in the kingdom by the Spirit is to believe in the Son of God, Jesus. What does it mean to believe in Him? First it means a belief in Jesus- Who He is as God’s only Son, --and what He did. Jesus came to die for all men. Jesus says in verse 14: “The Son must be lifted up that whoever believes in Him will have eternal life.” The “lifted up” is a short phrase for the act of Jesus dying on a cross as a substitute for men by paying for their sins in His own body. Those who believe Jesus—that this is what He has done for them, are given everlasting life and are said to be born again.
In summary, Hinduism teaches that born again is a part of an ongoing process of continual transmigrations of the soul through reincarnation. It happens to all creatures. Christ teaches that it only happens once to those who believe in Him.