A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
psa 14:1The practical atheism and total and universal depravity of the wicked, with their hatred to the good, are set forth. Yet, as they dread God's judgments when He vindicates His people, the Psalmist prays for His delivering power. (Psa 14:1-7)
Sinners are termed "fools," because they think and act contrary to right reason (Gen 34:7; Jos 7:15; Psa 39:8; Psa 74:18, Psa 74:22).
in his heart--to himself (Gen 6:12).
psa 14:2looked--in earnest enquiry.
understand--as opposed to "fool" [Psa 14:1].
psa 14:3filthy--literally, "spoiled," or, "soured," "corrupted" (Job 15:16; Rom 3:12).
psa 14:4Their conduct evinces indifference rather than ignorance of God; for when He appears in judgment, they are stricken with great fear.
who eat up my people--to express their beastly fury (Pro 30:14; Hab 3:14). To "call on the Lord" is to worship Him.
psa 14:7captivity--denotes any great evil.
Zion--God's abode, from which He revealed His purposes of mercy, as He now does by the Church (compare Psa 3:4; Psa 20:2), and which He rules and in which He does all other things for the good of His people (Eph 1:22).