Forgive my Ignorance

1. for-give
   /fərˈgɪv/ verb
   –verb (used with object)
   to grant pardon for or remission of (an offense, debt, etc.); absolve.
   to give up all claim on account of; remit (a debt, obligation, etc.).
   to grant pardon to (a person).
   to cease to feel resentment against: to forgive one's enemies.
   to cancel an indebtedness or liability of: to forgive the interest owed on a loan.
   
   verb (used without object)
   to pardon an offense or an offender.

forgive. (n.d.). Dictionary.com Unabridged (v 1.1).

I don’t understand how forgiveness works. I mean, I get how you can agree to let something go. But, that doesn’t mean that whatever occurred was OK. It just means you will try to get by it, right? But, does it also mean that when you think back on whatever occurred that it shouldn’t still burn your a$$? Because if it didn’t burn your a$$, that sort of implies that it (whatever action) was somehow OK or justified. Which it probably wasn’t. Which is why it upset you in the first place. But if it does still burn your a$$, then you haven’t REALLY let it go, have you?
OR
Not feeling resentment or upset about something that hurt you would imply a certain neutrality to the situation, an ability to disconnect from the events. Which if you were truly disconnected, likely would not have resulted in your state of offense. So, you wise folk of blog land, what’s the deal? How does forgiveness work? I can't seem to nail it down here.