Justice, in the context of this question, refers to another term for a judge. Judges, in law practice, refers to an individual who will conduct a trial before issuing a ruling regarding the trial itself. Judges tend to have a different role depending on the country since each country has a different judiciary system. The question, however, refers to the practice in the United States.
Generally, people with (D) conservative leanings would prefer judges who interpret the laws in a strict constructionist manner.