In Changing Lenses, Howard Zehr juxtaposes concise sketches of two different "lenses" through which we might consider justice:
Retributive Justice: Crime is a violation of the state, defined by lawbreaking and guilt. Justice determines blame and administers pain in a contest between the offender and the state directed by systematic rules.
Restorative Justice: Crime is a violation of people and relationships. It creates obligations to make things right. Justice involves the victim, the offender, and the community in a search for solutions which promote repair, reconciliation, and reassurance.
Obviously, one form of justice is more punitive and focused on the past, while the other can be transformative and focused on the future.
With roots in historical Community Justice and Biblical Covenant Justice, the goal of restorative justice is not to let an offender "off the hook", but to allow for conversations, in due time, which might make more transparent the needs of the victim as well as circumstances of the offender which may have led to the offense.
Additional information can be found on the Wikipedia page on Restorative Justice.