The basic idea is that instead of going to an Afterlife Human beings, perhaps also animals, sometimes even plants are reborn here on Earth or in some other realm. Those who believe in reincarnation believe that we don't just live one life and die once, we may die and be reborn numerous times.
Belief in reincarnation may be compatible with belief in heaven and/or hell. Heaven and hell may be places of rebirth where our souls or egos live till their next death and rebirth, Buddhism teaches this. Alternatively heaven may be a permanent reward for a very good life while lesser individuals experience reincarnation, Sikhism teaches this.
Some Christians believe in reincarnation and believe this is compatible with Christianity, others maintain that belief in reincarnation is incompatible with Christianity.