A living being is re-incarnated if after they die they start a new life in a different physical body.  (Carnate means to take a bodily form)

It is also called rebirth or transmigration.

Reincarnation as an ancient belief is based upon a living being having a soul, as the foundation of their being, which is eternal and/or a part of the universal spirit. If there is belief in the soul being the life-force within a body, then it is possible for that life-force to remain after death, and to be present in another body.

Most followers of the Abrahamic Religions do not believe that people reincarnate, despite the fact that Jesus Christ, a central figure in both Christian and Islamic faiths, ‘rose again from the dead in a new body’, and resurrection is a form of reincarnation.

One of the key obstructions to belief in reincarnation is the inconsistency with the the threat of eternal punishment. However belief in a higher power of love, “God is Love” as the Bible states, does not conflict with reincarnation.

Of course we now know that the human body is constantly changing, with all cells being replaced every seven years or less. So our physical body is not the same over time.

“Matter and spirit are forever bound together; divine and mortal forever interpenetrate and manifest one another. The changing of forms is called resurrection, and the return is called ascension, although to us it just looks like death.”

Richard Rohr

“Does anything survive the death of the body? Milton E. Brener responds with a resounding yes. He presents compelling case histories of people who have memories of past lives. Even those with little or no background in physics will be able to follow his logic. He has opened an intriguing discussion of the connection between quantum physics and reincarnation, leading to the conclusion that a mental, or what some would prefer to call “spiritual,” element of our being, does survive death.”
Clarion Reviews about ‘Our Quantum World and Reincarnation’ by Milton E. Brener

“The soul grows by reincarnation in bodies provided by nature, more complex, more powerful, as the soul unfolds greater and greater faculties. And so the soul climbs upward into the light eternal. And there is no fear for any child of man, for inevitably he climbs towards God.”

Annie Besant

“When this physical body is no more capable of functioning, energies do not die with it, but continue to take some other shape or form, which we call another life. … Physical and mental energies which constitute the so-called being have within themselves the power to take a new form, and grow gradually and gather force to the full.”

Buddhist scholar Walpola Rahula

“There is no question that when this physical body is no longer capable of functioning, the energies within it, the atoms and molecules it is made up of, don’t die with it. They take on another form, another shape. You can call that another life, but as there is no permanent, unchanging substance, nothing passes from one moment to the next. Quite obviously, nothing permanent or unchanging can pass or transmigrate from one life to the next. Being born and dying continues unbroken but changes every moment.”

Zen teacher John Daido Loori 

“”Reincarnation” normally is understood to be the transmigration of a soul to another body after death. There is no such teaching in Buddhism–a fact that surprises many people, even some Buddhists!”

Barbara O’Brien

According to Hinduism, a soul reincarnates again and again on earth until it becomes perfect and reunites with it Source. During this process the soul enters into many bodies, assumes many forms and passes through many births and deaths. This concept is summarily described in the following verse of the Bhagavad gita:

“Just as a man discards worn out clothes and puts on new clothes, the soul discards worn out bodies and wears new ones.” (B G 2.22)

“Do not wait for immortality. The resurrection of life is today.

Begin to live today as though you are an immortal being, and all thought of death and fear of change will slip from you.

I know that every apparent death is a resurrection; therefore today, gladly I die to everything that is unlike the good.

Joyfully I am resurrected into that which is beautiful, enduring and true. 

Silently I pass from less to more, from isolation into inclusion, from separation into oneness.”

Ernest Holmes (1938)