Originally Posted by Phage

Cynthetiq explained the significance of the sacrifice exactly as I understand it, but I would like to expand more about the original sin. When Adam and Eve ate the fruit they were departing from what God wanted them to do, e.g. sinning. Their offspring are not being blamed for the original sin, so much as the sinning they are doing because of their parents.

To put it in context of Cynthetiq's example the children are not branded as thieves because their father was a thief, they are thieves because their father was a thief, and are branded because of that.