Perhaps the place we should begin is by admitting that we do not fully know or understand. One New Testament writer acknowledged that when we explore God's Truth in the here and now "we see through a mirror dimly" - one day it will all be revealed. That is not to say that Christians are clueless about the events of the cross, but no-one can provide a precise explanation down to the last detail of why, by dying on a cross, Jesus made it possible for human beings to be re-united with God. That's why we described our beliefs as "faith" - we take God at His word, we are willing to believe that Jesus death was the one and only way that things could be put right between us and God.
But over the years we have developed many images and metaphors which help us better understand this profound truth. One of those is already hinted at in the text above, and expresses it in terms of crime and punishment. We know that there is wrong in the world, and we know that wrongdoing needs to be put right through some sort of penalty - Jesus paid that penalty, by accepting a punishment He did not deserve. Other images of healing, washing, purifying etc. have also been used - each helps to deepen and enrich our appreciation of God's loving sacrifice, but in the end we are simply called to accept in faith that this is God's way of putting things right.
But why do they need to be put right? - read on for further answers.