"We are justified freely by His grace through the redemption that came by Christ Jesus." (Rom. 3 v.24)
The word "justified" has often been explained as "JUST as IF I'D never sinned". While that's a great play on words, it's more like the definition of "forgiveness" than it is of "justification".
To "justify" means to "make right". In word processing, you "justify" your text by lining it up neatly against the margin, to make it look right. In the legal sense, "justify" is the opposite of "condemn".
In this tableau, you stand accused of not living up to God's standards. The Devil is the prosecutor, Christ is the defence, and God is the judge. God says to the Devil, "What evidence do you have against the accused?", and the Devil, with a gleam in his eye, unrolls a long scroll, full of the records of your misdeeds. It's so long that it drapes on the floor. The Devil is just about to start reading out from this long list when Jesus shouts out, "Wait - this person who stands here accused has been justified by his faith in me. There is no condemnation!" And before his very eyes, the words on the scroll melt away, and the Devil stands there aghast - because he has nothing to say. All our sins have been taken away, and then God stands to pass judgment. The courtroom is hushed as everyone waits to hear what He has to say
It is, to quote John Bunyan, "as if I had heard it thus expounded to me: 'Sinner, thou thinkest that, because of thy sins and infirmities, I cannot save thy soul, but behold, my Son is by me, and upon Him I look, and not on thee, and will deal with thee according as I am pleased with Him.'"
See also: How are we justified?