The question could be asked a different way? How does Jesus dying on the cross help me today? The best way to answer this is to think of an outdated practice called "debtor's prison". It basically works as follows.
When there is debt, of any kind, it must be paid. If someone owed money and they could not pay it, or if they committed a crime and could not pay restitution, they were cast into prison until it was paid. There would be a placard placed on the outside of the cell with their debt or crime written on it. Their family had to pay the debt to get their family member out. If that prisoner were to die while waiting on the debt to be paid, the next of kin would be cast into prison until the debt was paid. This would go on with more family members being cast into prison until the debt was completely paid. There were no exceptions; the debt had to be paid.
When Adam sinned, he created a debt. It was a debt that he could not pay. Sin is a debt and in order to have justice, it must be paid. In Genesis 3:15, God declares war on Satan. That is the first glimpse at the promise of a coming Messiah; one who could pay the debt of sin Adam owed. Jesus came and gave His life for a sinful world. The world is the people and His sinless life was the price to pay the debt off for them.
Where does it fit in with me? Well, since Adam is family, his sin, read that as debt, would have kept perpetuating down the line and eventually have fallen on me to pay. Since I could not have paid it, I would have been cast into prison with hopes a family member could pay it. By accepting the provision God provided for the debt, I am free from it and prison.
Need more proof? Here is the best part. Jesus was hanging on the cross and said seven very profound things. The best was in John 19:30. From the cross, Jesus proclaimed, “it is finished”. At first glance, He was pronouncing that the work was done as indeed it was. But, when we study the words in the original language? “It is finished” is translated from one Greek word; tetelastai. The definition? “Paid in Full”!
Now, once someone would leave prison, they would carry the placard with them for the rest of their days. Why? In case someone would say that they were, or their family was, supposed to be in prison to pay a specific debt. The placard would have “paid in full” written on it and sealed by the government, which in that day would have been their king.
The next time Satan tries to remind you that you or one of your family should be in prison to pay Adam’s sin debt, show him the placard that Jesus gave you. It is the Word and it says, “Paid in Full”!