This is called samsara.
Samsara is derived from "to flow together," to go or pass through states, to wander. Mostly a great revolving door between life and death and a new life reincarnated cycle of life. Also known as a game in ancient India.
Samsara is conceived as having no perceptible beginning or end. The particulars of an individual's wanderings in samsara are determined by karma. In Hinduism, moksha is release from samsara. In Buddhism, samsara is transcended by the attainment of nirvana. The range of samsara stretches from the lowliest insect (sometimes the vegetable and mineral kingdoms are included) to Brahma, the highest of the gods.
Depending on context, the details on samsara may vary: Hinduism, Jainism, Buddhism, Sikhism, Surat Shabda Yoga are a few philosophical traditions that are very similar but differ widely, however, in the terminology with which they describe the rebirth process (hence samsara) and in the metaphysics they use in interpreting it. However, in all these an ongoing cycle of birth, death, and rebirth is assumed as a fact of nature and it's referred to as 'samsara'.