Short answers, pulled from the story.
Saṃsāra in Buddhism is the beginningless cycle of repeated birth, mundane existence and dying again, considered to be suffering, or dukkha. It is perpetuated by desire and ignorance, avidyā, along with the karma and sensuousness that result.
Buddhist cosmology typically identifies six realms of rebirth in saṃsāra: gods, demi-gods, humans, animals, hungry ghosts and hells. Earlier Buddhist texts describe five realms instead, combining the god and demi-god realms into one.
Saṃsāra ends when a being attains nirvāṇa, or more broadly liberation, mokṣa, the extinction of desire paired with true insight into impermanence and non-self. Some texts describe this as the point when the transfer of consciousness from one life to the next finally ceases.
Saṃsāra is perpetuated by karma, which is caused by craving and ignorance, avidyā. The tradition's explanation shifted over time: earlier texts treated craving as the root cause, stilled through dhyāna, while later tradition identified ignorance as the deeper root.
Early Buddhist texts suggest the Buddha faced difficulty explaining what is reborn given the doctrine of no-self, anātman. The fifth-century scholar-monk Buddhaghosa compared rebirth to a flame passed from one candle to another, calling the mechanism rebirth-linking consciousness, or patisandhi.
Alternative translations of saṃsāra include conditioned existence (Daniel Goleman), cyclic existence (Jeffrey Hopkins), uncontrollably recurring rebirth (Alexander Berzin) and wheel of suffering (Mingyur Rinpoche).