"Just and the Justifier"
The most precious book ever written is the Bible. The most precious book in the Bible is Romans. The most precious chapter in Romans is chapter 3. The most precious verses in Romans 3 are verses 23–26. And the most precious four words in Romans 3:23–26 are "just and the justifier" (v. 26). So, then, the phrase "just and the justifier" are the most precious words and constitute the most precious phrase ever written in the entire history of the universe. And so, to understand the meaning of this phrase is (insofar as it means that a person understands the gospel) the most important single thing a person could ever do: more important than money, fame, family, happiness, friends, sex, education—indeed, than life itself. Let us now look at the phrase in its context.
23 for all have sinned and fall short of the glory of God, 24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus, 25 whom God put forward as a propitiation by his blood, to be received by faith. This was to show God’s righteousness, because in his divine forbearance he had passed over former sins. 26 It was to show his righteousness at the present time, so that he might be just and the justifier of the one who has faith in Jesus. (Rom 3:23–26 ESV)
Taken in context, this phrase is an absolutely huge and sweeping claim about God, redemptive history, Jesus Christ, and salvation. Leading up to it, Paul asserts that "all," i.e., both Jews and gentiles, are inadequate before God in that they "fall short of the glory of God" (see 1:23; Jn 12:32). But nevertheless, says Paul in v. 24 and the first half of v. 25, God justifies such sinful and inadequate people "through the redemption that is in Christ Jesus." Redemption was effected through Christ's propitiatory death (i.e., Christ was "put forward" by God as a sin-offering), which may be appropriated by means of faith.
"The times of ignorance God overlooked, but now he commands all people everywhere to repent" (Acts 17:30). See also Luke 18:14 and Galatians 3:11-13.