Therefore do not be anxious, saying, 'What shall we eat?' or 'What shall we drink?' or 'What shall we wear?' For the Gentiles seek after all these things, and your heavenly Father knows that you need them all. But seek first the kingdom of God and his righteousness, and all these things will be added to you. (Matthew 6:31-33)
The Gentiles, unbelievers who find their only existence in this present world with no thought of eternity or God's kingdom, seek intensely (επιζητουσιν) the physical and material things of this world. The Greek word used has the force of "craving." In Revelation, these people are labeled as "dwellers on the earth" (3:10; 6:10; 8:13; 11:10; 13:14; 17:2, 8 et al). This fallen world is all they have, so they crave all the pleasures of it they can get.
Jesus admonishes his disciples to think differently. And He promises His people, the citizens of His kingdom (Philippians 3:20), that our heavenly Father will provide all these things if we trust Him and focus on spiritual priorities.
In contrast to the intensive "seeking" or "craving" of the Gentiles for physical necessities and comforts, Jesus urges His disciples to "seek" (ζητεῖτε) the kingdom of God and His righteousness. The Greek particle translated "but" (δε) is not the strongest word that could have been used to express contrast. And since it is followed by adverb "first" (πρωτον) -- "but seek first" – it is clear that Jesus is not diminishing the importance of diligent work and wise management of resources. The Book of Proverbs, as well as Paul’s exhortations (Eph. 4:28; 1 Thess. 4:11), will certainly correct any misconception in that area. This verse is about priorities: Godly priorities relieve anxiety. Jesus says that the greatest possession we can have is our relationship to God -- citizenship in His kingdom and righteousness, Christ-like character. When our spiritual priorities are in order, we need not be worried, indeed, we will not be worried about our physical and material provisions. God cares for His own.