The concept of Rebirth exists only to certain characters whom have had gone through it's countless cycles, and had gained such knowledge through intuition. Currently, Lenega Zir and Darius Ralo are the only ones that have knowledge of the cycle.
When an entity dies, it's spirit leaves it's no-longer-functioning mortal vessel, and then goes to an afterlife that he/she/it creates themselves based on their mindset. If a person was bad, they will experience bad realities, while if a person was good, they will experience good. This is sometimes messed up, as some people that die, even though they may have led a good life, if they feel they have done more harm than good (even when they really didn't), they will also experience bad realities, even if they did not deserve it.
There are also instances where these afterlife experiences have been tampered with by an outside force or spirit, utterly changing what the spirit experiences. (Black / Yggdrasil is a good example of this. Even when he died and had done a lot of good in his time, he experienced what could be compared to be as Hell regardless of what he did in his lifetime. This insinuates that perhaps there is another entity working against certain spirits.)
Once a certain amount of time has been reached, and/or a number of spirits no longer re-enter the worlds as entirely new beings (Either out of choice or are physically unable to.), a new Cycle is created, and the current one ends. When a new cycle is created, every spirit of the previous reality is ported over to the new reality, and starts again. Within these cycles, whenever a spirit meets another spirit, they are destined to meet them again, despite if they lead entirely different lives or if their parting has been for multiple cycles.
A common misconception among new people that learn of the cycles are that the same events occur repeatedly without change. While this is false, there are certain groups of spirits that do get stuck within the same events over and over again. The causes for this to happen are quite a few, such as the groups of spirits are bound to the same cycle of events due to one major event that happened within that cycle that these spirits refuse to let go of until it has been resolved. (A conspiracy being such an example. Any spirits involved within that conspiracy that had impacted their lives in such a way that they refuse to let go of it even in later cycles will need the conspiracy to be solved before they can move on.) These spirits are called Hanging spirits.