Give justice to the weak and the fatherless; maintain the right of the afflicted and the destitute. Rescue the weak and the needy; deliver them from the hand of the wicked.
These verses show us what kind of societal impact God expects those in positions of power to employ. Let me dispense of the controversy of this psalm quickly. Psalm 82:1 pictures God poetically sitting in the "midst of the gods" exercising His sovereign rule. The little "g" gods are not polytheistic beings... they are instead human rulers. It is a hebraism to call them "gods". Jesus held this view and even quoted this psalm this way (see John 10:34-35). We have the exact same convention in English calling God "The Lord" and also in old monarchist terms referring to human leaders as "lords". Great Britain still has the House of Lords as a form of human government.
The real issue at hand in the psalm is just how human "lords" ought to rule over others. Human government tends toward corruption, injustice, and partiality due to our innate wickedness (Psalm 82:2). Hence the command of God for those people with the power to change things to really care about justice for the weakest members of society. God wants people to help the weak and to care for orphans. He wants us to guard the just and the right treatment for the poor and for the sick. He wants us to rescue those suffering at the bottom of human misery. He wants us to love His justice and act accordingly. In short, God wants human governments to act like Him with justice, mercy, and grace.
It is tragic that most Christians have given this passion for the poor and those in the worst suffering over to people who may not care for the neediest among us with Christ's compassion. The church must recapture that call to bring the gospel and the love of God to the lowliest. And we must insist for it in human governments around the world, expecting God's standards for our leaders and "lords".