Watching the material success of others can easily stir up feelings of frustration, jealousy, and doubt about living a moral life. A person walking an honest path may sometimes feel the world offers no reward for their choices, or perhaps the psalmist is directing this realization inward as a personal rebuke [אבן עזרא, ביאור שטיינזלץ, רד״ק]. The reassurance to live without fear does not address physical danger, but rather a gnawing anxiety and envy. The primary approach among commentators is that this serves as a warning against feeling bitter or jealous when watching someone else grow wealthy. The real danger of this envy is that a person might abandon the correct way of living and instead dedicate their life entirely to the pursuit of money [מאירי].
A deeper psychological perspective suggests a more specific scenario: a poor, righteous individual watching another righteous person achieve great wealth. The poor person might fall into a state of panic, worrying that his own lack of money is a sign that God is displeased with his actions. He is reassured not to be afraid, and to never interpret a peer's financial success as evidence of his own spiritual failure [אלשיך].
As a wealthy person's home fills with property, possessions, and luxuries [מלבי״ם], onlookers must remember that this is not a type of wealth worth worrying over. The modest amount God provides to the poor person will sustain him just as effectively as the vast fortune sustains the rich person, because every individual lives according to the specific portion allotted to them [מאירי, רד״ק]. Furthermore, one should not mistakenly believe that an abundance of assets represents true honor. When the wealthy person dies, he takes absolutely nothing with Him, leaving him with no advantage over the poor. The only genuine wealth a person can carry into the World to Come consists of good deeds and the charity they distributed. Material possessions left behind in the hands of strangers do not constitute true glory [מלבי״ם, רד״ק].