When Jesus used the analogy of being "Born Again", in the Gospel of John, I believe it's quite obvious what he meant. When I person is born into the world of human senses, he become aware of his body, other bodies and the physical existence that surrounds him like clothes, toys, etc. When he's born again, he discovers the spiritual world in much the same sense that a baby discovers his crib and parents.
Becoming spiritually aware is part of other religious practices like Buddhism. Somewhere along the way, one finds oneself in some kind of spiritual world. There are various rituals to help one transcend this world like mediation, soul travel and past life therapy.
In Christianity, the concept of rebirth seems to be related to water and spiritual baptism from the Holy Spirit. Something divine happens which opens one's eyes to the spirit world(i.e The Kingdom of God).
You don't need to be a Christian to jump into the spirit world. Many different religions have done that for thousands of years. Connecting to Christ is a different thing. It's a decision to be part of "his team". It's a decision to "mind meld" with the team leader and his brotherhood. Basically, this is the big "I AM" connecting up with the little "I ams".
Different religions have different ways of expressing themselves on the above subject. We should honestly try to understand the other guy's point of view.