Romans 3:21 (NKJV): But now the righteousness of God apart from the law is revealed, being witnessed by the Law and the Prophets.
In King James Version, it's written this way: But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets. The word 'righteousness' here is 'dikaiosune' (meaning 'justification') in Greek, from the word 'dikaios', which means 'right, justice, innocent, holy'. 'Apart from the law' because Jesus has already satisfied and fulfilled the law (Matthew 5:17) when He died on the cross, witnessed by the law and the prophecies from of old (say, from the prophet Isaiah).
Romans 3:22-24 then follows, '... even the righteousness of God, through faith in Jesus Christ, to all and on all who believe. For there is no difference; for all have sinned and fall short of the glory of God, being justified freely by His grace through the redemption that is in Christ Jesus, ...'
The word 'justified' here is 'dikaioo' in Greek (also from the word 'dikaios'), meaning 'to render you (or regard you) as innocent, just, free'. Imagine the judge in the court of law giving you a verdict, and pronounces you innocent and free. That's exactly who you are in God's eyes today! And this is all because of what Jesus Christ has done for you on the cross some 2,000 years ago! He took upon Himself your sins and your punishment, so that in exchange, you have His 'dikaiosune'. Now, does He deserve all these? No! Do you deserve His 'dikaiosune'? No! For all have sinned and 'fallen short'! A sin is a sin, and a sin has to be punished! Yet, knowing that you cannot save yourself (for the wages of sin is death - Romans 6:23), and because of His great love for you, He was willing to send His only begotten Son (Jesus) to die for you, so that His Son would take upon Himself your sin and punishment instead (John 3:16, Isaiah 53).
Romans 5:8-9 says, 'But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us. Much more then, having now been justified ('dikaioo') by His blood, we shall be saved from wrath through Him (Christ)'. So, today, as a believer, know that God is not angry with you any more, because you are in Christ! The Bible also says this is a gift from God (Romans 5:17-19), to be received by faith (i.e. a believing heart), knowing that we cannot earn it by ourselves.
Jesus Himself has also become the propitiation (i.e. mercy seat) for you (Romans 3:25-26). This word 'propitiation' can be translated as 'an atoning victim'. In other words, when Jesus died for you on the cross, He has also become the 'atoning victim' for you, so that you can be 'at-one' (reconciled and in right standing) again with God! (See also Leviticus 16:14-16 for the 'typology')
2 Corinthians 5:21 says, 'For He made Him (Christ) who knew no sin to be sin for us, that we might become the righteousness ('dikaiosune') of God in Him (Christ)'. King David saw this truth long before Jesus came, saying, "Blessed are those whose lawless deeds are forgiven, and whose sins are covered; Blessed is the man to whom the Lord shall not impute sin." (see Romans 4:7-8, Psalm 32:1-2) And today, as a believer, you are one of those whom King David spoke of those days!
Let's now cross-refer to the Old Testament. Isaiah 54:14 says, 'In righteousness, you shall be established; (and therefore) you shall be far from oppression, for you shall not fear; and from terror, for it shall not come near you'. Isaiah 54:17 then says, 'No weapon formed against you shall prosper, and every tongue which rises against you in judgment, you shall condemn. This is the heritage of the servants of the Lord, and their righteousness is from Me (the Lord)'.
Isaiah 41:10 (KJV) says, "Fear thou not; for I am with thee; be not dismayed; for I am thy God; I will strengthen thee; yea, I will help thee; yea, I will uphold thee with the right hand of My righteousness." This word 'righteousness' is 'tsedeq' in Hebrew, meaning 'right, just' (from the word 'tsadaq' meaning 'to be forgiven, made right, justified, clear, cleansed'). Also, 'right hand' here means 'the stronger part'. You know what? Today, this prophecy has come to pass, and He is now showing Himself strong to you and for you! And if He is for you, who can be against you? (Romans 8:31)
So, if you are believing God for healing to your body today, believe first that you are righteous (i.e. forgiven, made right, justified, clear, cleansed), and your healing shall flow (see also Psalm 103:3 - notice that forgiveness comes first, then healing). Guilt blocks healing to flow. Why are some people not getting healed? And sometimes even after confessing many healing verses from the Bible? The answer lies in the sense of guilt within that person (that sub-consciously causes him to think that he deserves his punishment). In short, a guilt-free life leads to a victorious life! So, let go of your past guilt, no matter how difficult it is to let go. His grace is sufficient for you, and He's here to help you (Isaiah 41:10).
Proverbs 4:18 then gives you a tremendous promise, saying, '... the path of the just (from the same word 'tsadaq') is as the shining light, that shineth more and more unto the perfect day' (KJV). The New International Version says it this way: 'The path of the righteous is like the first gleam of dawn, shining ever brighter till the full light of day'. And that's exactly what you'll see happening in your life, as you continue to be 'righteous-conscious', instead of 'guilt-conscious'!
No wonder Jesus Himself said these words: "But seek first the kingdom of God and His righteousness ('dikaiosune'), and all these things (i.e. all good things flowing) shall be added unto you." (Matthew 6:33) Believing, you'll have it. Amen!
Note: Being 'righteous-conscious' here is different from being 'self-righteous'. To be 'righteous-conscious' is also to know that it's by faith (believing heart) that we are made righteous (i.e. justified). It's His righteousness being imputed on us (i.e. laid upon us), not self-earned; and it's by His grace (His ability) that we have it, not ours.