Both Buddhism and Hinduism believe in an (almost) endless cycle of births, known as samsara. They also both seek release from this cycle of rebirths.
Hindus believe in an everlasting soul (atman) that is reincarnated more-or-less intact from birth to birth. Through spiritual practice, Hindus seek release (moksha, also known as liberation) so that the soul can join with the Universal Divine Force (Brahman, often simply translated as God).
The Buddha, however, taught that there wasn’t a constant soul, but a collection of feelings, perceptions, senses, and other intangibles that made up all living beings. The concept of the lack of a constant sould is known as anatta.
Hence, for Buddhists, the ultimate goal is something more abstract: ending suffering by escaping the cycle of rebirths, and entering into a state of Nirvana. It is a common misconception to translate Nirvana as meaning “Paradise,” or as “Heaven.” Nirvana itself is something of an abstract concept. One meaning is “cool,” which implies that one is far away from the fires of desire and Kilesa (defilement).