A person suffering through deep distress is often compared to someone sitting in complete darkness. To escape this state, the prayer asks for a divine light that will drive away the shadows and bring success and rescue [רד״ק, אבן עזרא]. The primary approach among commentators is that this request borrows a common image from human relationships. Just as a person greets someone they care about with a bright and happy expression, asking God to shine His face is a plea for Him to look down with compassion and goodwill [מצודת דוד, מאירי].
This plea for a shining face also carries a very specific vision for how the rescue should unfold. Rather than asking God to act out of anger and destroy the pursuers, the prayer focuses entirely on receiving God's positive attention. The radiant light of God's favor directed at the sufferer is powerful enough on its own to strike fear into the enemies and ensure a safe escape [אלשיך]. Furthermore, this request seeks an open and visible display of divine care. When the rescue is clear for all to see, it honors God in the world and proves that those who turn to Him will not be disappointed [מלבי״ם].
Ultimately, the appeal rests entirely on God's endless kindness [מלבי״ם]. The prayer asks for salvation as an act of pure charity, acknowledging that the individual might not actually deserve to be saved based on their own actions [רד״ק]. By asking for this rescue as a free gift of kindness, the hope is that receiving God's help will not deduct from any personal merits the individual has already earned [אלשיך].