Reincarnation is the belief that when one dies, one's soul is reborn in a new body. This is a central tenet of Hinduism and Buddhism and is also found in other religions and tribal societies. There are debates around what exactly is reincarnated - the soul? consciousness? The majority of Abrahamic religions like Christianity and Islam do not believe in reincarnation, seeing life as linear with an afterlife, rather than cyclical rebirth.

1. Reincarnation
Reincarnation is the religious or
philosophical concept that the soul or
spirit, after biological death, begins a
new life in a new body that may be
human, animal or spiritual depending on
the moral quality of the previous life's
actions. This doctrine is a central tenet of
the Indian religions and is a belief that
was held by such historic figures as
Pythagoras, Plato and Socrates. It is
also a common belief of other religions
such as Druidism, Spiritism, Theosophy,
and Eckankar and is found in many tribal
societies around the world, in places such as Siberia, West Africa, North America, and
Australia. Although the majority of sects within the Abrahamic religions of Judaism,
Christianity and Islam do not believe that individuals reincarnate. The word
"reincarnation" derives from Latin, literally meaning, "entering the flesh again". The
Greek equivalent metempsychosis (μετεμψύχωσις) roughly corresponds to the common
English phrase "transmigration of the soul" and also usually connotes reincarnation after
death, as either human, animal, though emphasising the continuity of the soul, not the
flesh.
http://en.wikipedia.org/wiki/Reincarnation
Reincarnation is the belief that when one
dies, one's body decomposes but
something of oneself is reborn in another
body. It is the belief that one has lived
before and will live again in another body
after death. The bodies one passes in
and out of need not be human. One may
have been a Doberman in a past life,
and one may be a mite or a carrot in a
future life. The belief in past lives used to
be mainly a belief found in Eastern
religions such as Hinduism and
Buddhism. From a philosophical point of
view, reincarnation poses some interesting problems. What is it that is reincarnated?
Presumably, it is the soul that is reincarnated, but what is the soul? A disembodied
consciousness?
http://www.skepdic.com/reincarn.html

2. Natural life is cyclical. Day fades into night
and turns back into day as the sun rises.
One season gradually gives way to the next.
Over the passage of time, new generations
are born and old ones die. The continuous
succession of birth, death and rebirth
permeates nature even though our own
lives seem linear. So it's no surprise that
some ancient observers looked at the
seeming linearity of human existence and
decided that life, like the natural world,
might actually be more cyclical than linear.
Multiple religions, philosophies and
movements adopted this belief in cyclic life,
or reincarnation. Reincarnation, also called
transmigration or metempsychosis, is the
concept that the soul, or some aspect of the
soul, is reborn into new lives. Depending on
the religion or philosophy, the soul can
appear incarnate in humans, animals or
plants as it works its way toward an eventual escape from the cycle of birth, death and
rebirth. Most religions that believe in reincarnation consider it the path to purity and
salvation. Reincarnation is widely accepted by the major Eastern religions -- most
prominently Hinduism and Buddhism. It also has a history in ancient Greek philosophy.
However, for people more familiar with the major monotheistic religions -- Christianity,
Judaism and Islam -- the idea of reincarnation seems foreign and maybe even a little
strange. That's because Christianity, Judaism and Islam conceive of time linearly. Life is
simply a short step that determines the quality of an afterlife. For those who believe in
only one life followed by an eternal afterlife, reincarnation is like an unwieldy marathon
run by relay instead of a short, concise sprint.
http://people.howstuffworks.com/reincarnation.htm