Is it, “I wish I could change the past, and if I could, I would have acted differently?” I don’t think that’s all of it, because that begs the question, “Why?”
Is it, “I acted in some way that is objectively morally wrong?” I don’t think that’s it either, because who’s to say what is objectively right or wrong?
I think, in its truest sense, “I’m sorry” means, “I feel pain because you feel pain.”
It is a way to validate one another. That validation alone is important. It is made all the more important by the further statement, “I’m sorry, and I won’t do that again.” It is a way of saying, “I wish to avoid the pain I feel because of your pain, so, I will not act in a way to cause you pain.”
Everything we do comes down to this: feelings, needs. Feelings, needs.
What good does remorse do anyone? It does the good of feeling someone else’s pain with them. Validation. And, maybe, a change in one’s behavior in the future.