How does reincarnation fit into Buddhist teachings and beliefs?
This is a complex question. Buddhism believes in the Oneness of all life. All sentient beings are equal which means all living things have Buddha-Nature, the potential to become a Buddha.
Thus, all life is to be honored and respected. Oneness is like Lake Michigan.The lake is one body of water. But a wave can form and we see it. It has a shape and form, for a limited amount of time. But when the wave crashes into the shore, we no longer see it.
Nonetheless, the water that makes up that wave is always part of Lake Michigan. It had the form of a wave for a short time and then returned to be part of the overall lake again.
Human life is like that wave. We have a shape and form for a limited period of time. It is our temporary ego that thinks it is separate from the Oneness. The reality is that we come from the Oneness, and we return to the Oneness—and we are never really separate from the Oneness.
The complex part of this question depends on how one defines “reincarnation.”
The first thing to remember is that Buddhism does not have the same belief as the Hindu religion, which has the concept of direct reincarnation into another being.
But there are several Buddhist cultures that have a basic teaching that there is a level of punishment or reward that results from behavior, which sounds like reincarnation.