As I have just said in a post above, the power and authority that the flesh has over us ceases. Because the marriage one has to flesh ends at the death of that husband. Your flesh doesn't literally die, of course (not yet). It's figurative language used to describe how the Holy Spirit in you has removed the power and authority of the flesh as though it is dead, likening it to the death of a husband who once exercised his power over a wife by the authority given him by the law of marriage. With husband 'flesh' not deceased (as I have just described what that means) its power and authority over you to bear it's fruit (sin) ends and you are now free to be married to Jesus Christ and bear his fruit, the fruit of righteousness.
Romans 7:2,4
2by law a married woman is bound to her husband as long as he is alive, but if her husband dies, she is released from the law that binds her to him.
4So, my brothers and sisters, you also died to the law through the body of Christ, that you might belong to another, to him who was raised from the dead, in order that we might bear fruit for God.
Romans 6 explains how knowing this with certainty and in faith is the key to overcoming sin and no longer having to submit to it. It's how we can say to sin, "not tonight, honey, I have a headache." The law no longer being able to enforce a marital relationship you are no longer in because of the 'death' of the flesh.
Romans 6:11-12
11count yourselves dead to sin but alive to God in Christ Jesus.
12Therefore do not let sin reign in your mortal body so that you obey its evil desires.