We must not view reincarnation as a mere belief from eastern religions. It has to do with the cyclic nature of everything in this world. It is a most fundamental fact about how the soul, or consciousness, can cyclically be present in this world, which it isn't a natural part of.
Consciousness is not of time, as we have said, is not bound by time. But to grow within this temporary world, and to become eventually fully conscious in this (physical-psychical) world, it must incarnate in this world. It must use a vehicle that belongs to these (physical-psychical) dimensions, through which it can gradually become more conscious. And this vehicle is necessarily temporary. It is born and will inevitably die. This is why the soul has to reincarnate, again and again, over very long planetary cycles, until its expansion through matter is unhindered by matter, that is, until it has become capable of being fully conscious, fully awake, as itself and not as ego.
The conditions in which we reincarnate, such as who are our parents and surroundings, in what part of the world we are born, the quality of physical and psychical bodies we have, etc., are all the result of various cause and effect relations the soul is involved with, and very possibly limited by. But, from one series of incarnations to the next, the soul normally becomes freer of such karmas, and is reborn more and more in an overall context where matter becomes a means by which consciousness can expand, rather than a means by which it is limited and emprisoned.