Compassionate feelings for someone that make it easier to forgive that person for some offense can be called forgiveness. Feelings of forgiveness make it easier to feel empathy toward people who have harmed you.
If you give someone a break and forgive some misdeed or mistake, you are practicing the act of forgiveness. If your sister borrows your favorite white sweater without asking, it's easy to offer her forgiveness. If your sister borrows your favorite white sweater without asking and spills a glass of chocolate milk on it, forgiveness may be a little harder to grant.