"For if, because of one man's trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ." Romans 5:17
I find this concept to be just a little difficult to grasp, but basically I believe it's saying that Adam's sin introduced death which has reigned ever since, but God's grace through the victory of the cross introduced life, and through this grace, life can reign in us.
I do not, however, think that this verse is saying that we are somehow guilty of Adams offence - I, for one, know that I have more than enough offense of my own, and the penalty I face is due to my own sin, I'm sure, and not poor old Adam's, who as far as I can tell, only slipped up once. However, Adam's offence was the first among many, and as such, introduced sin into the world, sin of which we have all been guilty, each in our own way, and only through God's precious grace can we be free from the deadly consequenses of that sin and live a life in relationship with God - the kind of life we were designed to live with him...the kind of life where righteousness reigns through grace...the only kind of life that truly is life.
That's the life I want, Father. I give up all I am to you, my Lord, and my life is yours. Help me to live that life. Grant me your daily mercies and fill me with your grace. Give me your righteousness...not based on the law, but based on your love and grace through Jesus. I love you, Lord.