The aim of man should be to achieve moksha, the end of the birth-death cycle. The concept of reincarnation is closely tied to this. That is, the atman is held back from self realization through the attachments formed during one’s lifetime and is therefore reborn after death in another body. As the Gita says, like a person discards one garment for another, the atman leaves one body for another.
The concepts of reincarnation and moksha are subtly different from reincarnation and nirvana in Buddhism. But the essence of vedantic and buddhist teaching are similar to the extent that both seek to end the birth-death cycle through actively seeking truth.
Another crucial concept in Hinduism is that moksha can be obtained through multiple means. These are action (karma), devotion (bhakti) and knowledge (jnana). Advaita Vedanta advises one to follow the path of knowledge, of course. But it also teaches that the three paths are mutually compatible.