The word "Sorry"

Sorry - feeling regret, compunction, sympathy

How powerful IS the word "sorry"?
When you say sorry, does the recipient appreciate the torment and courage you mustered to apologise? Will things really be resolved and reset from scratch?
Does the recipient understand the intense emotional trauma before one says the word "sorry"?

Sorry carries with it a sense of hope and fear.
Hope because you hope it will take all unhappiness, discomfort and anger away.
Fear because you fear it will backfire and you now have to accept the certainty of the anger.

It's even an intricate decision-making process simply because of the extremities of the possible outcomes.