"Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be. As the embodied soul continuously passes, in this body, from childhood to youth to old age, the soul similarly passes into another body at death. A sober person is not bewildered by such a change." - Bhagavad Gita
The word reincarnation comes from Latin and literally means, "entering the flesh again". In Greek philosophy, the closest term describing reincarnation is metempsychosis and it corresponds to the common English phrase "transmigration of the soul.” As evident the terms connotes reincarnation after death in a new physical form of human, plant, animal or any other tangible object, and emphasize on the continuity of the soul (and not the flesh.)
The Buddhist concept of reincarnation rejects the idea of soul, and spirit, and only accepts the "stream of consciousness" as a link between all forms of life, and across five or six realms of existence, including the human, any kind of animal and several types of supernatural being.