One of the most widely accepted definitions of justice is "the administering of deserved punishment or reward" and in Mosiah 15:9 & 27 it talks a lot about "justice" and how Christ stands between it and us, how He satisfies the demands of justice, and also how He cannot deny justice when it has its claim.
I've been thinking about how justice and mercy work with the Savior. He not only makes it possible for us to not have to endure the full punishment for our sins, but He works to make restitution to those who have been hurt. Often we like to think that when we do something it will only affect us. But most of our choices do affect others, for good or bad. And whether we intentionally or inadvertantly hurt someone else perfect justice would demand not only a punishment for us but also restitution for those we have injured.
It is amazing that Jesus is able to fulfill all of the requirements of justice. He not only stands between us and justice, thereby relieving us of the pain of the full punishment, but He also makes things better for those who have been adversely affected by our sins. His atonement reaches out to heal them and make them whole once again, making a perfect restitution that no human could ever come close to.
If I were to relate it to our legal system, imagine someone who has robbed someone else. The perpetrator would be brought before the judge and probably sentenced to time in prison, regardless of how sorry they were or the reasons behind their actions. This might bring some small relief to the victim by knowing that the person is locked up and is paying for their crime. But it wouldn't really bring restitution because the perpetrator would likely not be required to repay the victim, and there would be no real way for him to bring back the feelings of safety or security that would have been lost by the victim. Even when our justice system works the way it's set up to it isn't perfect.
Contrast this with how it might work with Jesus. If that same person was caught and brought before the judge (assuming he was truly sorry) Jesus would step in and offer to pay back what was taken and He would also serve the prison sentence. In return the perpetrator would agree to pay Jesus back by doing whatever Jesus asked him to (like community service.) BUT... even with this we have the problem of the victim not feeling completely satisfied by justice, especially when they see the guilty one being let off easily and not being punished to the fullest. And this is what I love- Jesus also reaches out to the victim and makes them whole. He doesn't just offer to replace the stuff that has been lost, He is able to restore their peace of mind, their feeling of being safe and secure. Jesus doesn't overlook the victim in order to give mercy to the sinner. His atonement reaches out and offers healing to both.
Jesus knows every detail of every situation in our lives. He knows our thoughts, our intents, and our desires. He is willing to step in and apply mercy while still satisfying the demands of justice, and He is forever reaching out to us to heal us when we have been the victim.
On the flip side, Jesus cannot deny justice its claim when someone refuses to accept His offer of mercy. He can't force someone to believe in Him, and to be able to enjoy the blessings of repentance and forgiveness we have to believe in Him and follow Him. I'm sure that He would gladly step in at a moment's notice to offset the penalties of justice if the offender would reach for Him in faith. But He cannot do so by force. He must let justice have its claim. His ways are perfect.