Reincarnation; the Hindu understanding. Image by the Himalayan Academy, from Wikipedia - original url. Copyrighted to Himalayan Academy Publications, Kapaa, Kauai, Hawaii. Licensed for Wikipedia under Creative Commons License cc-by-sa-2.5 and requires attribution when reproduced.
The following is from Wikipedia ( original url - GNU Free Documentation License) and gives a decent overview. i'm repeating it here to save "reinventing the wheel" :-):
In India the concept of reincarnation is first recorded in the Upanishads (c. 800 BCE), which are philosophical and religious texts composed in Sanskrit.
According to Hinduism, the soul (atman) is immortal, while the body is subject to birth and death. The Bhagavad Gita states that:
Worn-out garments are shed by the body; Worn-out bodies are shed by the dweller within the body. New bodies are donned by the dweller, like garments.
The idea that the soul (of any living being - including animals, humans and plants) reincarnates is intricately linked to karma, another concept first introduced in the Upanishads. Karma (literally: action) is the sum of one's actions, and the force that determines one's next reincarnation. The cycle of death and rebirth, governed by karma, is referred to as samsara.
Hinduism teaches that the soul goes on repeatedly being born and dying. One is reborn on account of desire: a person desires to be born because he or she wants to enjoy worldly pleasures, which can be enjoyed only through a body. Hinduism does not teach that all worldly pleasures are sinful, but it teaches that they can never bring deep, lasting happiness or peace (ananda). According to the Hindu sage Adi Shankaracharya - the world as we ordinarily understand it - is like a dream: fleeting and illusory. To be trapped in Samsara is a result of ignorance of the true nature of our existence.
After many births, every person eventually becomes dissatisfied with the limited happiness that worldly pleasures can bring. At this point, a person begins to seek higher forms of happiness, which can be attained only through spiritual experience. When, after much spiritual practice (sadhana), a person finally realizes his or her own divine nature —ie, realizes that the true "self" is the immortal soul rather than the body or the ego—all desires for the pleasures of the world will vanish, since they will seem insipid compared to spiritual ananda. When all desire has vanished, the person will not be reborn anymore.
When the cycle of rebirth thus comes to an end, a person is said to have attained moksha, or salvation. While all schools of thought agree that moksha implies the cessation of worldly desires and freedom from the cycle of birth and death, the exact definition of salvation depends on individual beliefs. For example, followers of the Advaita Vedanta school (often associated with jnana yoga) believe that they will spend eternity absorbed in the perfect peace and happiness that comes with the realization that all existence is One (Brahman), and that the immortal soul is part of that existence. The followers of full or partial Dvaita schools ("dualistic" schools, such as bhakti yoga), on the other hand, perform their worship with the goal of spending eternity in a loka, (spiritual world or heaven), in the blessed company of the Supreme being (i.e Krishna or Vishnu for the Vaishnavas and Shiva for the dualistic schools of Shaivism).