Adam was our representative, our federal head in the Garden, when he fell in the Garden, we fell, being in Adam. The last Adam, Jesus Christ, is the representative, the Federal Head of those He died for, His. sheep.
12 Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned-- 13 for until the Law sin was in the world, but sin is not imputed when there is no law. 14 Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come.
15 But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many. 16 The gift is not like
that which came through the one who sinned; for on the one hand the judgment
arose from one
transgression resulting in condemnation, but on the other hand the free gift
arose from many transgressions resulting in justification. 17 For if by the transgression of the one, death reigned through the one, much more those who receive the abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ.
18 So then as through one transgression there resulted condemnation to all men, even so through one act of righteousness there resulted justification of life to all men. 19 For as through the one man’s disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous.(Romans 5)
When Adam sinned, that guilt was passed on to all his posterity, the whole human race. Through no fault of our own, we were born with the sentence of death placed upon us by Adam's sin.
When Jesus lived on this earth, He lived a perfect, sinless life. It was only after He was imputed our sins(Matthew 26, 2 Cor. 5:21, Isa. 53:6, 1 Peter 2:24, Heb. 9:28) that He stood before His Father in our place and took the full force of His Father's wrath. He then rose from the dead for our justification(Rom. 4:25). When we are saved, all that He is, and all that He did, was imputed to us. His sinless life He lived has been imputed unto us, and the Father now sees us as if we never broke on Law. Why? Our sins have been covered by the blood and we are draped in the righteousness of Jesus Christ.