A prayer for true justice hinges on the reality that human beings can easily fake an outward appearance of goodness. Absolute justice requires a judge who can see past the surface and evaluate the hidden inner self.
The prayer asks for an immediate end to evil. The primary approach among commentators is that the evil itself will ultimately consume the wicked. The very plots and malicious thoughts they initiate will turn against them, acting as their accuser and bringing about their complete downfall [רד"ק, אבן עזרא, שטיינזלץ, מצודת דוד]. In a historical context, this request is directed specifically at King Saul and his men who relentlessly pursued David [המאירי]. However, another perspective views this as a prayer for repentance, hoping that the wickedness and sins will vanish from the world, allowing the people themselves to change their ways rather than face destruction [אלשיך, אבן עזרא].
In sharp contrast to the ruin of the wicked, there is a plea to firmly establish the righteous. This concept is compared to the final, stabilizing phase of constructing a building, ensuring it stands securely on its foundation [מלבי"ם]. This support is meant to help the righteous along their path [רד"ק, מצודת דוד, שטיינזלץ]. David makes this request for himself, for the righteous among the people of Israel, and specifically for the secure establishment of his own royal throne [רד"ק, המאירי].
Ultimately, only God can execute absolute justice. While many people project a positive image that hides their true nature, God examines the most deeply concealed thoughts [רד"ק]. The human anatomy, specifically the kidneys, is used as a metaphor for a person's deepest and most guarded secrets [אבן עזרא]. Because God possesses complete knowledge, He does not need an external courtroom or legal process to determine who is right. He simply looks within and knows when a person's heart is completely loyal to Him [שטיינזלץ, מצודת דוד].
This reliance on God's ability to search the heart also addresses how David can confidently call himself righteous in his bitter conflict with Saul. David is not claiming to be inherently better than anyone else. Instead, he surrenders the final judgment to God, the only one who truly knows who is in the right [אלשיך, המאירי]. God is recognized as a perfectly just judge, entirely free of corruption, who treats every person exactly according to their innermost thoughts [רד"ק, המאירי]. This absolute justice is so central to His nature that being righteous is not merely an adjective describing Him, but one of God's actual names [רש"י].