Way back in Mitzvah #79, we were warned not to take pity on the poor and powerless in a court case. Here we are told about the opposite scenario, not to favor the rich and powerful.
It’s easy to see both sides. On the one hand, one might say, “I feel bad for the plaintiff, he has nothing, I’ll rule in his favor since the rich defendant can afford it.” On the other hand, one could also say, “This defendant is a pillar of the community, he does many good works, I can’t afford to alienate him by ruling against him.” Both of these are wrong. The case is to be judged on the facts alone. Sometimes the rich and powerful man will win and sometimes the poor and humble man will win. (In my example, I made the poor man the plaintiff and the rich man the defendant but it could be the other way around. Rich people are less likely to sue poor people, though; they have no money.)
This mitzvah requires the judges to treat both parties equally. For example, either both parties may sit or both parties must stand (Talmud Shevuos 30a).
The reason underlying this mitzvah is as we have said: just courts are needed to run a just society. Corrupt courts are unacceptable regardless of whom they favor in their bias.
This mitzvah applies in all times and places. It is discussed in the Talmud in the tractates of Shevuos (30a-b) and Kesubos (106a). It is codified in the Shulchan Aruch in Choshen Mishpat 17. This prohibition is #275 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #70 of the 194 negative mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.