Merriam-Webster dictionary defines Righteousness as the state of being and acting in accordance with divine or moral law, and being free from guilt or sin. If that is true, then the breastplate of righteousness from a Christian perspective is being right with God -- following His laws and His principles.
It makes sense that the breastplate of righteousness is not something seen, but an attitude and a holy lifestyle that every Christian must personally enact. In Ephesians 6:10:12, the Word says, "We don't wrestle with flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places." With this in mind, it is futile to fight using human logic and human strength, and it is necessary to see the real enemy, not the person or people Satan has used to break hearts and wound or kill a Christian's spirit.
A prophecy in Isaiah shows that the breastplate of righteousness was first modeled by Christ. "He saw that there was no man, and wondered that there was no intercessor; therefore His own arm brought salvation for Him; and His own righteousness, it sustained Him. For He put on righteousness as a breastplate, and a helmet of salvation on His head; He put on the garments of vengeance for clothing, and was clad with zeal as a cloak."
Since there was no man able to intercede for Christ or offer redemption, he interceded for himself and offered his own salvation. Jesus clothed himself with armor as a soldier who was going into battle against his enemies. If Jesus found the breastplate of righteousness necessary, then there is no doubt that Christians today should deem this piece of armor a personal requirement.
The breastplate of righteousness is available and accessible because God shares Himself with believers. What He has, He gives in order that Christians have the power to resist the evil and corruption in today's world and so they have everything they need to promote the light of the gospel to the unsaved.
To put on the breastplate of righteousness, Christians must learn to live without sin and to know who they are in Christ. They should be bold in asking God for help, protection and provision. Believers should pray and intercede for themselves and on behalf of others, and be willing to take off worldly layers and replace them with the good things of God. In doing so, the breastplate of righteousness will keep hearts pure and spirits alive.