The idea behind forgiveness is that we have this concept that when we are wronged or believe we're wronged, a moral debt is incurred and the perpetrators owe us moral reparations. Now, what if the person hates me or doesn't even know me? Well, this is a moral debt that will never ever be repaid.
Over time, you end up with a mile long list of moral debts you are tracking—incurred by strangers who don't even know you, politicians, anonymous social media posters, unrepentant criminals. You let the people you hate live rent-free in your head using a debt they never intend to repay.
So why keep track of it?
By forgiving them, you say that you'll forgive that moral debt and stop keeping track of it, instead entrusting the judgment of Christ, and freeing yourself to look towards the future rather than dwell on the worst parts of the past.
If she truly forgives the assassin, Erika prevents him from consuming her life and is able to stop the destruction of grief.