Reincarnation is probably the most difficult topic for me to cover in this series because it is the most alien to my culture, but, perhaps foolishly I'll give it a try anyway because it's something a significant number of people believe in and I think there are lessons in it for all of us.
Most modern Christians reject the concept of reincarnation because the larger church always has. We're learning now though, that reincarnation was a concept shared by many early, pre-Constantine, Christians in one form or another. Since we can't posit any theology as undeniable fact, perhaps it's wise to inform ourselves of all of them, even if we've already chosen the one that suits us best.
The basic tenet of reincarnation is that, like most religions, there is a greater form of life beyond this physical one, and each of us is invested with some aspect of it. There is a spirit that invests the physical body and survives it when the body dies.
What separates reincarnation from other religious beliefs is that they believe the spiritual form inhabits the physical form to improve and perfect it through a process called "karma", and when the physical form dies, the spirit moves on to another physical form to continue the process of perfecting the karma.
Part of this, I think, comes from observation. When one thing dies, other things are born. Even in cases of massive destruction, like the eruption of Mt. St Helens, the process of rebirth begins almost immediately.
If one believes that some physical forms are invested with a spirit, then it's not an unreasonable stretch to believe that all physical life is invested with a spirit. This also prevents the hubris that comes with believing we're the only creatures blessed with such an endowment.
There is a trap here to be avoided where a person might get the idea that they do better in life because their karma is superior and it's acceptable when bad things happen to people, because it'll all be corrected in the next iteration of incarnation. The correction is that hubris is bad for your own karma and should be avoided, lest you be the person bad things happen to next time.
Many forms of reincarnation believe that eventually the spiritual form reaches a point where it can exist entirely separate from the physical world in something similar to the Abrahamic concept of heaven. This answers the question many people have of why there would be a physical world if the spiritual world is all that really mattered.
So, what to make of all this? Perhaps there is a difference between spiritual energy and the individual personality we consider our spirit form.
What if we possess not just one individual spirit, but a million, each one sharing the experience known as our lives. When we die, some of these spirits could move on to plants or animals or some could combine with other spirits in new people and some still could move on to the purely spiritual plane we call heaven.
Each would be still fully and completely "us", but after we die they would scatter through the universe to occupy new forms and fulfill new purposes. Grandma would still be looking down on us from heaven, but she would also be a part of the grass beneath our feet, the birds in the air and the new baby we hold in our arms.