The ability to forgive those who have caused you harm or betrayed you is the most important virtue in The Lion, the Witch, and the Wardrobe. People who are unable to forgive small slights find themselves drawn into a spiral of negative emotions. In order to be redeemed, they must find pity and sympathy for their fellow creatures somewhere in their own hearts. Good is able to triumph over evil through one great act of mercy and compassion. Forgiveness, when it comes, is complete. What's done is done, and it would be pointless to bring up past wrongs.
Although Aslan redeems Edmund, he does not actually forgive Edmund's transgression against his siblings.
By sacrificing himself for Edmund, Aslan implies that all Edmund's past behavior is forgiven and Edmund can begin with a clean slate.