Matthew 5:6 hunger and thirst for righteousness
This is the opposite of the self-righteousness of the Pharisees. It speaks of those who seek God's righteousness rather than atempting to establish a righteiousness of their own. Romans 10:3 states that "For they being ignorant of God's righteousness, and seeking to establish their own righteousness, have not submitted to the righteiousness of God." Ignorant both of God's inherent righteiousness revealed in the law and the rest of the Old Testament (which should have shown the Jews and us... our own unrighteousnes s) and of the righteousness which comes from HIm on the baiss of faith.
Righteousness is the state or condition of perfectly conforming to God's perfect law and holy character. Only God is inherently righteous (Deut. 32:4; Job 9:2; Psalms. 11:7; 116:5; Roman 3:10; 1 John 2:1; Rev. 16:5). Man falls woefully short of the divine standard of moral perfection. But the gospel reveals that on the basis of faith - and faith alone - God will impute HIs righteousness to ungodly sinners.
... their own righteousness - is based on their conformity to God's law and often to the less demanding stands of their own traditions. I see this in a few of the Hmong Christian Churches. This balance of tradition and trying tot conform to God's law.
Philippians 3:9 states that "And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:" (KJV) or as stated in the New Century Version: "and to belong to him. Now I am right with God, not because I followed the law, but because I believed in Christ. God uses my faith to make me right with him."
... not having my own righteousness from the law... this is the proud self-righteousness of external morality, religiousritua l and ceremony, and good works. It is the righteousness produced by the flesh, which cannot save from sin. ... faith in Christ is the confident, continous confession of total dependence on and trust in Jesus Christ for the necessary requirement to enter God's kingdom... and that requirement is the righteousness of Christ, which God imputes to every believer.
What they seek will fill them, for instance, it will satisfy their hunger and thrist for a right relationship with God.