Verses: Romans 4:23-25 (NIV)
The words “it was credited to him” were written not for him alone, but also for us, to whom God will credit righteousness—for us who believe in him who raised Jesus our Lord from the dead. He was delivered over to death for our sins and was raised to life for our justification.

When we are being justified through the act of another, it means we are being held blameless for something we did wrong because someone else stepped in and assumed responsibility for whatever it was that we did.  Jesus did that for us.  He took responsibility for our sins because we repented and asked Him for forgiveness.  Being justified is as if we had never done that wrong thing.  We have a clean slate.  Because of Jesus, we have been made holy or righteous in the eyes of God – opening up the door for us to have a relationship with Him.