The word "reincarnation" derives from Latin, literally meaning, "entering the flesh again" An alternate term is transmigration implying migration from one life (body) to another.
Reincarnation refers to the belief that an aspect of every human being (or all living beings in some cultures) continues to exist after death, this aspect may be the soul or mind or consciousness or something transcendent which is reborn in an interconnected cycle of existence.
The transmigration belief varies by culture, and is envisioned to be in the form of a newly born human being, or animal, or plant, or spirit, or as a being in some other non-human realm of existence.
There are many religions (Jainism, Hinduism, Buddhism, within Judaism, the Zohar, Taoism, Norse mythology, Sikhism, African Vodun, Native Americans, Islam, Druze, Wicca and various spiritualism philosophies i.e; Theosophy, Modern Astrology, Anthroposophy, Scientology, the 19th century Christian Spiritism philosophy) that believe in reincarnation.
However, the interpretation of this belief is quite broad.
In Christianity the common belief is supported in the notion of the Rapture. Although the word “Rapture” is not a biblical term, its meaning refers to the 1st advent of Christ who returns to receive all those who believed and accepted Him as the Christ during their lifetime.
Whether you are dead or alive at the time of His coming, the body is miraculously reintegrated if dead, into its original form and if alive, your body is instantly transformed so that is no longer blond in it.
This blood is referred to as corruption, which is to say that an eternal body if it does not have blood, does not die. Making this part of the transformation a significant aspect, as blood is sacred to God.
Believers than meet Jesus in the clouds and are whisked away into Heaven where they await the battle of Armageddon. Much like the Norse belief in Ragnarok.
The biblical support for this event is first seen in Ezekiel 37:1–14
1 Thessalonians 4:13–17
13 But I would not have you to be ignorant, brethren, concerning them which are asleep, that ye sorrow not, even as others which have no hope.
14 For if we believe that Jesus died and rose again, even so them also which sleep in Jesus will God bring with him.
15 For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep.
16 For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first:
17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
1 Corinthians 15:51-53
51 Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed,
52 In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
53 For this corruptible must put on incorruption, and this mortal must put on immortality.
Although Christianity does not consider this aspect of the resurrection as reincarnation, the strictest definition of reincarnation, which is..
“the belief that an aspect of every human being continues to exist after death”
Does in fact apply!