Something or someone that is unjust is just not fair. An unjust boss might fire you the very first time you're late for work.
You might think of the word justice in order to remember the meaning of the word just, which means "fairness or righteousness." An unjust judge does not play by the rules; he might send a person to jail even though there isn't enough evidence that a crime was committed. Unjust behavior is improper or dishonest: "The professor acted in an unjust manner when he gave everyone an F just because there was a rumor that his students didn’t like him."