The next piece of armor is described in the New Living Translation as the "body armor of God's righteousness." I like that. This clearly teaches that the only "righteousness" that God accepts is His own shown through His Son, Jesus Christ. Paul emphasizes this in both Romans 10:1-4 and in Philippians 3:9. Therefore, the body armor we are to wear is the righteousness given to us through Christ. That is, the righteous standing we have before God we received when we put our faith in Christ. Romans 3:22 NLT says, "We are made right with God by placing our faith in Jesus Christ. And this is true for everyone who believes, no matter who we are."
God's righteousness gives us a proper "standing" with Him, thus it paves the way for us to call upon God when we face each battle and we are able to receive from Him all the resources we need to face Satan.
Also, having God's righteousness, we have a secure place to stand when Satan tries to deceive us with his lies and tries to make us think we're not "good enough" for God. Our response to that is that we're not relying on our goodness but on the goodness of Christ Himself! And Jesus IS Good Enough for God!!
Also, wearing God's righteousness shows that we're not "self-righteous" before the world. Nothing turns people off to the Gospel than a self-righteous Christian! The kind of righteousness we have in Christ keeps us humbly relying on Him and keeps us from acting proud and boastful.