Radak #1: He will not favor Gedolim and Ashirim in their case against the poor.

Radak #2: If this refers to Mashi'ach, "Lo l'Mar'eh Einav Yishpot" (Yeshayah 11:3).

Malbim: Mishpat is fixed; Tzedek is according to the particular need. Sometimes one veers from straight Mishpat to do beyond the letter of the law, according to the time, place, matter and litigant. He will judge the nation in general according to Tzedek, and not always stick to Torah law, if Tzedek obligates veering from it. E.g. if an Ashir merits against an Oni in Mishpat, but not based on Tzedek, he forces the Ashir to go beyond the letter of the law. However, he judges Aniyim b'Mishpat, according to Torah law, and does not make them go beyond the letter of the law when they cannot due to their poverty.