As Steve notes, this is a theory of the atonement - an explanation as to why Jesus Christ died on the cross and how it makes a difference for human's relationship with God. It assumes that a judicial punishment has to be administered somewhere in order for it to be possible for God to forgive us, or to have any relationship with us. In this theory, all human beings are guilty of sin, this means they are faced with the penalty of death. The only way God in his love can rescue human beings from this fate is to provide a perfect substitute - Jesus Christ - whose death is acceptable replacement for ours.
Two obvious problems:
- If God is omnipotent, why is he bound to follow a set of rules. Surely the rulemaker isn't subject to a law outside him, or he wouldn't be God? If his love is the overriding power (and the PS theory acknowledges this) then why is all this trouble necessary. Who's telling God He has to follow this procedure?
- We die. Genesis 3 teaches that mortality is the consequence of human sin. This is taken up by the PS theory and Jesus' death rescues us from death. But wait a minute, we remain mortal even having received the benefit of the cross. And if the death Gen 3 and Rom 6:23 refer to is spiritual death and not just biological, then that provides two more problems. a) did Jesus die spiritually, because if he didn't, he hasn't gone through everything condemned humanity must face and b) spiritual death sounds more like annihilation than any kind of ongoing existence in hell.
The problem is that all theories of what the cross means fall short of the reality. They can only be metaphors which cast light on the cross but cannot convey the whole meaning. Any theory fails if it is extrapolated to its logical conclusion.