1. This is one of two, twin psalms that speak of the fool who does not believe in God. The other is Psalm 54.
It seems anachronistic to imagine actual atheists of the sort we have today. That would have been virtually unheard of at that time. More likely are individuals who do not fear any reprisal from God. These fools are corrupt.
2. Romans 3:12 draws on Psalm 14:3 (53:3). "All have turned away, all have become corrupt; there is no one who does good, not even one."
This is the verdict of the LORD as he looks down from heaven (14:2). The psalm itself seems to be speaking parabolically, for the psalmist does not seem to include himself among those who are corrupt. Rather, fools devour God's people and never call on the LORD (14:4). The psalmist thus seems to be indicting evildoers rather than every last individual. Indeed, he goes on to mention the righteous (14:5) and the poor who are oppressed (14:6).
3. The final verse, which urges for salvation to come out of Zion, is a plea for the restoration of Israel, for God's people to be restored. This fact suggests it was written after the divided monarchy, perhaps even after the exile.
4. While Psalm 14 primarily refers to God as YHWH, Psalm 54 refers to him as Elohim, corresponding to two strands that also appear in Genesis.
These verses indicate God's opposition to the perverse, the wicked, and scoffers. By contrast, God's favor is on the upright, the house of the righteous, and the humble oppressed. The wise get honor, the foolish shame.
Psalm 1 and Proverbs 1:1-7
Psalm 2 and Proverbs 1:8-14
Psalm 3 and Proverbs 1:15-19
Psalm 4 and Proverbs 1:20-27
Psalm 5 and Proverbs 1:28-33
Psalm 6 and Proverbs 2:1-5
Psalm 7 and Proverbs 2:6-15
Psalm 8 and Proverbs 2:16-22
Psalm 9 and Proverbs 3:1-4
Psalm 10 and Proverbs 3:5-12
Psalm 11 and Proverbs 3:13-18
Psalm 12 and Proverbs 3:19-26
Psalm 13 and Proverbs 3:27-31