In a culture that inverts those preferences, it's an acknowledgment of a new debt of reciprocity. "I recognize that you're negatively impacted and ask you let me make you whole again"
We're in a bit of a weird and untenable cultural moment right now, where we allow anyone to call themselves a victim and insist that some other admit to an internal feeling of contrition. When that contrition isn't sincerely felt, which is natural in many cases, that's when we end up with both the vacuous and passive agressive "sorry you feel that way" and the equally vacuous and performative public apology.
In a world where we focus more on exrtrinsic actions and reciprocity rather than making demands of each others internal state, both forms of vacuousness go away: people do step on each others feet now and then, as happens, but the stepper helps the stepped find their footing again and both move on with their lives.