For Abraham, the relationship between faith and justification was because Abraham believed in God (faith) and lived his life for God, he was justified, or in good standing order with God. For us, it is the same thing, we must believe and trust in God, with our lives, surrender totally to him, and we are then justified or "right" with God. We are living according to God's will.
To me, justified means that we are doing what we are supposed to do, living according to God's word. When we live in sin, we are not in God's favor or living according to His will.