Who was delivered for our offences, and was raised again for our justification. Romans 4:25 KJV

What is justification (Righteousness)?

Romans 4:25 states that Jesus raised for our justification.

Justification by belief (faith) of Jesus (Galatians 2:.15-16). Jesus was delivered for our trespasses and was raised for our justification (Romans 4:25). 

Well, we were all dead with no hope of life because Adam and Eve chose to go with the word of Satan (to sin, to die) instead of sticking with the word of God (justification).

We understand that the resurrection of God makes it possible for mankind to escape the inevitable and irrevocable penalty of sin (disagreement with God), which is death.

John 3:16 explains the necessity to believe in Jesus: to not perish but have eternal life. And Apostle Paul states that our belief is worthless if Jesus was not risen.

Under the guidance of Romans 4:25, John 3:16 promises justification if we believe in Jesus. The justification comes from the resurrection and it empowers mankind to try again and again until they attain 100% obedience to God ant to not worry about the irrevocable death for the past failures (Ezekiel 33:13-20).

Therefore, justification commutes the death penalty for the past sins of the believers in Jesus who enroll in His plan of salvation which seeks those who become holy (Hebrews 12:14) and completes the program with a perfect 100% grade(Revelation 3:20-21) in order to be ultimately sanctified (made holy, made just, marked) by Jesus for eternal life.

Romans 5:16-20 ASV
(16) And not as through one that sinned, so is the gift: for the judgment came of one unto condemnation, but the free gift came of many trespasses unto justification [righteousness, δικαίωμα].
(17) For if, by the trespass of the one, death reigned through the one; much more shall they that receive the abundance of grace [favor] and of the gift of righteousness [abstract justification, δικαιοσύνη] reign in life through the one, even Jesus Christ.
(18) So then as through one trespass the judgment came unto all men to condemnation; even so through one act of righteousness [justification, δικαίωμα] the free gift came unto all men to justification [righteousness, δικαίωσις (declaring to be, verdict)] of life.
(19) For as through the one man's disobedience the many were made sinners, even so through the obedience of the one shall the many be made righteous [just, δίκαιος].
(20) And the law came in besides, that the trespass might abound; but where sin abounded, grace [favor] did abound more exceedingly:

Belief in Jesus we are justified no longer in the works of the Law.

Galatians 2:15-21 ASV
(15) We being Jews by nature, and not sinners of the Gentiles,
(16) yet knowing that a man is not justified by the works of the law but through faith in Jesus Christ, even we believed on Christ Jesus, that we might be justified by faith in Christ, and not by the works of the law: because by the works of the law shall no flesh be justified.
(17) But if, while we sought to be justified in Christ, we ourselves also were found sinners, is Christ a minister of sin? God forbid.
(18) For if I build up again those things which I destroyed, I prove myself a transgressor.
(19) For I through the law died unto the law, that I might live unto God.
(20) I have been crucified with Christ; and it is no longer I that live, but Christ liveth in me: and that life which I now live in the flesh I live in faith, the faith which is in the Son of God, who loved me, and gave himself up for me.
(21) I do not make void the grace of God: for if righteousness is through the law, then Christ died for nought.

Jesus marks us as righteous or just because we believe in Him and follows Him at 100%.

Romans 10:10 ASV
(10) for with the heart man believeth unto righteousness [justification, δικαιοσύνη (abstraction)]; and with the mouth confession is made unto salvation.

Note that belief does not save. The role of belief in Jesus is to allow us to take advantage of the justification (righteousness) brought about by the resurrection if we stood firm and overcame (Revelation 3:20-21, Hebrews 3:5-6,14).

Hebrews 3:5-6 ASV
(5) And Moses indeed was faithful in all his house as a servant, for a testimony of those things which were afterward to be spoken;
(6) but Christ as a son, over his house; whose house are we, if we hold fast our boldness and the glorying of our hope firm unto the end.
Hebrews 3:14 ASV
(14) for we are become partakers of Christ, if we hold fast the beginning of our confidence firm unto the end:
Revelation 3:20-21 ASV
(20) Behold, I stand at the door and knock: if any man hear my voice and open the door, I will come in to him, and will sup with him, and he with me.
(21) He that overcometh, I will give to him to sit down with me in my throne, as I also overcame, and sat down with my Father in his throne.