i spent a few years studying and practicing Tibetan Buddhism, so I feel I have some small understanding of their ideas.
Karma is the idea that every event has a cause (an idea science shares). A person's Karma is a direct result of thoughts, feelings, and behaviors they engaged in previously. When Karma ripens, you experience the consequences of your previous actions. People who engage in non-virtuous and unskilled actions experience what they perceive as negative Karma, and when they engage in virtuous actions, positive outcomes also result. There is a direct connection between one's actions and the consequences one experiences. It's like God's judgment without the need for God. Karma is like an algorithm for God's judgment for those who want to put God in there somewhere.
In this short lifetime, not all of our past Karma is going to ripen. Further, there are many things that happen that don't seem to be connected to any past behavior. Non-Buddhists rely on this to engage in non-virtuous behavior today because they believe they will dodge the consequences of that behavior in this lifetime. People also endure suffering when inexplicable events turn out against their wishes.
To overcome those problems, the Buddha embraced the prevailing Hindu beliefs in reincarnation, the idea of recycling since Beginningless Time. He posited that we have all cycled through birth, aging, sickness, and death an infinite number of times. At some point during one of those previous lives, we've participated in every possible non-virtuous act, and if something seemingly negative and random happens in this life, it's entirely due to non-virtuous behavior you engaged in during some past life.
Why is that useful? If you believed that everything that occurs happens due to your past Karma, you don't ponder "why" something happened. You just immediately accept it and move on, a much better spiritual state. Speculating on "why" something happens is a doorway to suffering. You will never find a satisfactory answer, and the quest for such an answer leads to suffering. The only way to avoid that rabbit hole of suffering is simply not to go down it. A sign on the doorway to that rabbit hole reads, "it's your past Karma." If you accept the wisdom of that sign, you will accept what is, and you won't waste any time trying to answer an unanswerable question that only causes suffering. If you don't have that wisdom, you will go down that rabbit hole over and over again and suffer needlessly in the process.
The Buddha turned what was considered a common-sense belief in reincarnation prevalent in his culture and turned it into a mechanism to avoid suffering and guide behavior toward virtue. It was a brilliant idea.
Of course, some deep thinkers of the time pointed out there are some ontological issues with the idea. If the self is merely an ephemeral group of ideas in your mind (which it is), what exactly survives death, and how does Karma pass from lifetime to lifetime? Not all Buddhist schools come up with the same answer, but the Tibetan Buddhists and many other Buddhist traditions embrace the idea of the Very Subtle Mind.
To many Buddhists, you have a Gross Mind, a Subtle Mind, and a Very Subtle Mind. The Gross Mind is what you experience in ordinary consciousness. The Subtle mind is akin to a light dream state where you can still have awareness of mental activity, and Tibetans developed a Dream Yoga to experience and explore this idea. However, the Very Subtle Mind is posited as the mechanism for carrying Karma.
I imagine the Very Subtle Mind like a punch card. It contains none of the memories or experiences of your past life, but it records all the Karmic imprints created by your thoughts and actions. You take this punch card with you from life to life, and when Karma ripens, the actual cause was from some past imprint carried by the Very Subtle Mind.
Obviously, this can't be tested, so the existence of a Very Subtle Mind is based on Faith alone. It posits a mechanism for cause and effect that carries emotional benefits for those who chose to believe it (you don't ask why bad things happen.) If you reject the Very Subtle Mind, reincarnation, and the ideas associated with it, you remove the sign from the rabbit-hole of suffering that comes with speculating on "why" bad things occur. Without that sign, many people go down that rabbit hole again and again and suffer the consequences.
You could look at the Very Subtle Mind like we currently view String Theory. Both of them posit untestable mechanisms, but if you explore what they offer you may find something valuable that comes from the idea.
Do I believe the Very Subtle Mind exists? Ontologically, no, I don't. But I live my life "as if" it exists because it helps guide my behavior, and it greatly reduces my suffering when shit happens. I think that is a mark of a good ethical system.
