Psalm 14 teaches the safety of godliness and peril of ungodliness. It is almost the same as Ps 53, the repetition emphasising the importance of its truths. It begins by describing the sad condition of men who reject God: "The fool has said in his heart: “There is no God” (v1a). In Hebrew, it is: "The fool has said in his heart: “NO God”or "no God for me." Thus, it's not just talking about atheists, who foolishly deny God's existence, despite all the evidence (Rom 1:19-20), but include those who reject His presence, light, voice and rule in their heart, as they want to be free to be their own god. God put the knowledge of the truth of God in their heart, but they suppress His voice saying 'No! God' (Rom 1:18,21, 25, 2:15). How foolish to reject God, their Creator, the Source of all goodness, love and light in their inner being! As a result, their foolish hearts are filled with darkness (Rom 1:21) and corruption (v1b). Having rejected their God-given moral compass (conscience), that points to God, they lose their sense of right & wrong, and worship created things instead of the Creator (Rom 1:23,25), and in time even call good things evil, and evil good (Rom 1:32, Isa 5:20), becoming moral fools, lacking sensitivity & insight of right & wrong (Rom 1:22). Thus (1) they are fools to say 'No' to God, and also (2) saying 'No' to God makes them into fools (corrupted in their inner moral being which is manifested in their lifestyle: "They have done abominable works (sins of commission). There is none who does good (sins of omission)” (v1c, Rom 1:24-31). Next there is a twist, for we think that the fool (v1) is a certail kind of man, but now God declares in v2-3, that this describes all mankind in our fallen state (depravity), for without His saving grace, we're all lost in darkness under the power of sin. In v2, God looks down to see if any understand the truth of God and seek Him (to know Him), the opposite of saying 'No, God!' In v3, He gives the results of His investigation: “(1) They have ALL turned aside" (from God, saying 'No' to God). As a result (2) "They have all together become corrupt (in their nature, the word describes rancid milk). (3) There is NONE who does good. NO, NOT ONE.” This 3 part description corresponds perfectly to the description of the fool in v1. Thus, this declares the depravity of all men in Adam. v1-3 are quoted in Rom 3:9-12 as a key part of his proof that the whole world is guilty before God and so can only be saved by grace thru Jesus. The Doctrine of Depravity is also seen in Ecc 7:20, Luke 11:13, Eph 2:1-3.
God coming down to investigate mankind (v2) is reminiscent of His judgments at the Flood, Tower of Babel and Sodom & Gomorrah. Before judgment, He always provides a way of salvation (grace), and saves those who turn to Him in faith. In v4, He addresses those who've rejected God's knowledge and grace, and have not called on Him to save them. He describes them as being ripe for judgment, workers of iniquity, who in their covetousness "eat people like bread" (exploiting the poor & helpless, treating people as expendable consumables, with little regret or remorse). Instead of praying to and seeking God, they prey on the helpless. God asks: "Have they no knowledge (of God)?" (v4). That is: "Don't they realise God will hold them to account and judge them?" Then v5 describes their day of judgment when God manifests Himself to them: "THERE (sham) they are in great fear." Jehovah Shammah = the Lord is THERE (present). So this declares that one day they will stand in God's Presence and then they will be in great awe and fear (lit: 'tremble in terror'). The parallel verse in Ps 53 says: “There they are in great fear (terrified with terror), where no fear was." God will especially judge them for persecuting His people, who take refuge in the Lord (v4-6).
He responds to this revelation from God with a prayer for salvation: “Oh, that the salvation (lit: Yeshua) of Israel would come out of Zion! When the Lord brings back the captivity (and restore the fortunes) of His people. Let Jacob rejoice and Israel be glad” (v7). This has a 2-fold fulfilment in the 2 Comings of the Messiah. From the context, the main captivity from which we need salvation is our captivity to sin. So, this is a prayer for the Messiah (Yeshua) to come from the heavenly Zion to the earthly Zion to save us from our sins - fulfilled in His 1st Coming. Only when we trust in Him will our fortunes be restored. Sadly, Israel rejected her Messiah and His salvation from sin, so her fortunes were not restored at His 1st Coming. But by the end of the Tribulation, she will trust in Yeshua, and call on Him to come out of Zion to save her from physical captivity and destruction at the hands of the antichrist, and restore her fortunes. He will return in response to this prayer and Israel will be established as the most blessed nation in the Millennium, when she will rejoice and be glad in her God.