What is the hindu and buddhist concept of the soul?

The word "Samsara" means literally "continuing on", "wandering on". It signifies the repetitive cycle of birth, ageing, death and rebirth.
Now though Buddhism and Hinduism share the concept of rebirth, the Buddhist concept differs in details from the Hindu doctrine. The doctrine of rebirth as understood in Hinduism involves a permanent soul, a conscious entity which transmigrates from one body to another. The soul inhabits a given body and at death, the soul casts that body off and goes on to assume another body. The famous Hindu classic, the Bhagavad Gita, compares this to a man who might take off one suit of clothing and put on another. The man remains the same but the suits of clothing are different. In the same way the soul remains the same but the psycho-physical organism it takes up differs from life to life.

The Buddhist term for rebirth in Pali is "punabbhava" which means "again existence". Buddhism sees rebirth not as the transmigration of a conscious entity but as the repeated occurrence of the process of existence. There is a continuity, a transmission of influence, a causal connection between one life and another. But there is no soul, no permanent entity which transmigrates from one life to another.

He man remains the same but the suits of clothing are different. In the same way the soul remains the same but the psycho-physical organism it takes up differs from life to life.