Just as we discard old clothes and
Put on new (clothes).
In the same way (we) discard old bodies
(And we) obtain new bodies.
Bhagawad Gitā, II. 22.
We believe that the soul leaves the body at the time of death and takes up another body (reincarnates). We are all evolving spiritually and take many births until we have no desires and all Karma- s resolved. Then our Ātmā (soul) merges with Paramātmā ( Brahman, God) and attains liberation from the cycle of birth and death ( Moksh). Everyone, even an animal, is entitled to Moksh.
If at the time of death we have any unfulfilled desire or unresolved Karma then we take birth in a new body. We are born in a family and under circumstances according to our unresolved Karma-s and unfulfilled desires. This gives us the opportunity to progress spiritually.