The term actually comes from an encounter Jesus had one night with a man named Nicodemus. (You can read about it at the beginning of the third chapter of John's Gospel.) Nicodemus was a very religious man, but in spite of that he apparently sensed something was missing in his life, and he thought Jesus might have the answer.
Jesus replied by telling him that all his religious deeds wouldn't save him -- nor can they ever save us. Our problem is that we are sinners, and no matter how good we are, we can never wash away sin's stain on our souls. God's standard is nothing less than perfection -- and we will never be perfect in God's eyes by our own efforts.
Instead, Jesus said, we need to be born again -- that is, God Himself needs to come into our hearts by His Holy Spirit to cleanse us and renew us. And God made this possible by sending His only Son, Jesus Christ, into the world to be the final and complete sacrifice for our sins. When we open our hearts and lives to Him, God's Spirit washes away our sin and gives us a new life as part of God's family.
Don't depend for your salvation on your good works, or your church membership, or anything else you might do. Instead, realize what Jesus Christ did for you by His death and resurrection, and invite Him into your life today. Then, the Bible says, you will be "born again... through the living and enduring word of God" (1 Peter 1:23).