We all find ourselves in positions where we need to forgive and be forgiven. We are on both sides of the coin. We forgive so that others and God will forgive us.
Often, we need help from Heavenly Father and Jesus Christ to forgive others. Concentration camp survivor Corrie ten Boom found she had to ask God to help her at one Sunday service. A former prison guard approached her and asked for her forgiveness. She didn't want to forgive him, but she prayed for help. She felt the feeling of forgiveness flow through her arm as she shook the man's hand. She no longer felt bitterness toward him. Similarly, we can pray to receive help to forgive others and ourselves.
Part of forgiving is having empathy for others. While reading the second book in the Ender's Game series, Speaker for the Dead, I realized more about empathy. Ender spoke the whole truth about the dead--the good and the bad. Most people are a mix of good and bad. This helps us realize that when we forgive, we look for the good in the other person.
We forgive in order to move forward. As Abraham Low says, we "excuse rather than accuse for our own mental health." Forgiving lets us redirect our former negative energy of holding a grudge into positive energy.
So often, spouses, family members and friends offend us, whether purposefully or accidentally. We let bitterness build with every small offense since we live with these people every day. But we need to let go of the bitterness in order to love those who we really love the most.
Note: Forgiving others does not mean returning to a dangerous person or a dangerous situation.
Here's a great article on forgiveness https://www.lds.org/ensign/2014/01/choosing-to-forgive?lang=eng