Reincarnation is not a Buddhist concept.
Reincarnation is the idea that the same soul or same person is reborn in successive bodies. Buddhism rejects the notion of a soul or a self that is permanent. You will never be reborn as the same person ever again.
What Buddhism teaches is rebirth, the cycle of birth and death. You may carry over into your next life karma, or traces, of your former lives, but you will be a new, unique person with no real memory of the past. According to Buddha-dharma, it’s very rare to remember a past life.
The concept of reincarnation found its way into Buddhism through the assimilation of folklore and native beliefs; strictly speaking, it is not part of the Dharma or teachings.
Ultimately, it doesn’t matter. Whatever happens when we die is going to happen regardless of what we believe. Buddhism does not stand on assertions about what comes after physical death. Buddhism is about the experience of life, here and now.
The great Zen master Dogen once said, “This present birth and death itself is the life of the Buddha. If you attempt to reject it with distaste, you are losing thereby the life of the Buddha.”