The most common kind of reincarnation teaching comes from Hinduism and Buddhism, and are based on the laws of karma. Karma says that what one sows in this life will be reaped in the next. Every action in this life has a consequence. BUT, the big difference with Christianity and reincarnation beliefs is when we come to the afterlife. The Bible teaches that the spirit and soul of humans is disembodied after death, awaiting resurrection.
Reincarnation is an intermediate state, but resurrection is an ultimate states.
Hope this helps, Bob.