If Buddhists don't believe in a soul, what exactly gets reincarnated?

Thank you.

But, that begs the question, what's the difference between one's consciousness and their soul? They seem like the same thing to me.

The other day I had to write a report for my humanities class and was given a list of religions to choose from. I picked Buddhism because I've recently met a ton of Buddhists and realized I get along with most of them. I wrote it from the standpoint of the soul being reborn and then realized after that there was no soul and had to go back and amend things, but couldn't find any answers about what it was that was being reborn. 

On the flip side, I also read that some people aspire to be reborn in the god realm, purely because it's like the Christian concept of heaven. Seems to go against the very foundation of the religion, but I'm no scholar. *shrugs* 

I agree that it's remarkably difficult to discern a difference.
The dictionary definition of a soul is minimalist:
either 1. the spiritual or immaterial part of a human being or animal, regarded as immortal;
or 2. an emotional or intellectual energy or intensity, especially as revealed in a work of art or an artistic performance.
In Western theologies, enough of the person remains in the soul to be capable of sentience, hence suffering or happiness - this definitely implies consciousness.

In popular Western fairy tales and culture, ghosts carry the personality, memories, and desires of the deceased person and act accordingly. I think possibly a lot of people absorb these ideas in their infancy and unconsciously retain the idea that personality and soul are inextricably enmeshed.

I should probably explain that there are different levels of Buddhism.
One is the religious. Broadly speaking, as a religion Buddhism carries as much superstition and myth as any other faith - with endless variations depending on which country one visits. People who are born into Buddhist cultures and raised without any deeper education in the sutras (Buddhist texts) will tend to believe in karma, souls and reincarnation in a very superstitious way: "I inherited lots of money due to my good karma in a past life therefore I deserve it/ that dog bit me and now I've got rabies because I was cruel to it in my last life, therefore I deserve it."

The other level is that of the serious and educated practitioner, one who practices the Eightfold path as a normal part of everyday life.
It is the view as spoken by Gautama Sakyamuni (the Buddha) himself. It is not religious because it is not dependent of faith and can be experienced directly through meditation. 
According to the sutras, whenever a follower or monk asked a question about the soul, Gautama would give one of two answers:
1. Such questions are irrelevant to the path to happiness,
or 2. if a belief is beneficial to the majority of people do not discourage it.
After his death, it was decided by the Sangha (at that time, a congregation of 500 hundred of his life-long followers)
that the belief in a soul and reincarnation had more positive effects than negative because it encourage people to live ethically and with generosity.
(Cynically and to be fair - this had beneficial results for the monks as one of the rules was that they could only live by begging -
if no one donated food, they were compelled by their vows to starve, even to death.)

For myself as a meditator - I would say that there is no soul.
In meditation I have observed that consciousness is only ever present when one is conscious of something,
and that something is a sense-based perception.
This includes consciousness of mental phenomena such as thoughts and memories.
In Buddhism, the mind/brain is viewed as the sixth sense door.
I accept that there are relative levels of consciousness, such as alpha, beta, dreaming, sleep, and coma.
Coma is the only state that I can have no memory of the experience of.

I would put it this way --
Who a person is consists of a combination of innate temperament (genetic), conditioning (cultural, familial, experiential combined with personal interpretation). It is a mix of memories, habits of mind and emotion, beliefs, desires, plans, fantasies etc. All these are conditional - meaning they are conditioned by and dependent on the person's circumstances. Thus, it is highly unlikely that they could exist independently of such conditions.
One can observe this in meditation. Alternatively, there is research in psychology and neuroscience which tends to confirm it -- although such sciences acknowledge that these studies are still in their infancy.
All personality is dependent on consciousness; it cannot exist without access to memories and conditioned mental reactions and processes.
Consciousness is only possible due to the food, water, air and hence energy that the body supplies to the brain and its metabolic processes.
Thus consciousness can only arise in a living person or animal. As soon as life ceases, there is no energy to supply the process of consciousness, hence all sentience, memory, desires and personality are extinguished.
It is my belief that this is one of the realisations that dawns as enlightenment develops - and that this is one of the reasons why the enlightened practitioner is said to be liberated from the rounds of reincarnation.


This post was edited by inky at April 5, 2019 11:10 PM MDT