The Hebrew word for "justification" is sadeq, which means "to do justice, vindicate, acquit, prove right". Another Hebrew word, zakah, also means justification, but in the sense of "to be clear, clean or pure".
Justification seems to be the focus of Pauline doctrine. Justification by atonement was the preferred theology of the Catholic Church. During the Reformation, the Protestants rejected atonement as the focus of justification and adopted God's grace as the focus... that we are saved by God's grace alone, regardless of what you do. The problem with the traditional Protestant theology of God's grace is that it is conditional... it is conditioned on our believing in Jesus Christ and accepting him as our "savior".
The Protestant Chrisitian view of God's grace is confusing. Grace by its very nature is unconditional. It simply exists as a result of God's love for ALL his creation. Once you start going down the road of... "It's free, EXCEPT that you have to ACCEPT it", then the unconditionality of it all is diluted.
Note that the concept of justification did not originate with Paul. The use of the the word justification that Paul knew as a Jew was in verses such as...
Isaiah 45:25 - "In the Lord all the offspring of Israel will be justified"
Isaiah 53:11 - "the Righteous One, My Servant, will justify the many..."
The meaning seems to focus more on "justice", rather than "personal redemption".
The Greeks words for justification are dikaioo, dikaioma, dikaios, dikaiosune, dikaiosis and dikaios, which mean "right, acquittal, righteous, righteousness, justify, justification"