Jesus' words are a call for faith. Rather than have our primary focus on the physical things of life which are needed (food, clothing, shelter, etc.), the Lord would have us focus first and foremost on His kingdom and the way of righteousness. Human philosophy would tell us that we cannot even begin to consider things spiritual until we've satisfied the necessities of life, our need for protection, and secured our social standing in the world. According to some, only after every other human need is met, should be we begin to consider our spiritual needs.
Now, don't misunderstand Jesus' words. He is not saying we should focus on the spiritual to the exclusion of the physical. We are told, "...if a man shall not work, neither shall he eat" (2 Thessalonians 3:10), and again, "...if anyone does not provide for his own, and especially those of his household, he has denied the faith and is worse than an unbeliever." (1 Timothy 5:8). How then do we fit these two verses with the thought presented by the Lord in Matthew 6:33?
Our focus is to be firstly on things spiritual, but not such that we fail in our physical responsibilities. There are two extremes, which I have seen, and I am convinced that the truth is in the middle. I met and studied with a young man a few years back who would not so much as lift a hand to search for a job. He had a family, whom he was separated from at the time, whom he was not providing for. He believed that if he studied and studied, and focused strongly upon things spiritual, that God would provide a job for him, and would provide for his family until such a time occurred. I've met others who have no time to attend the assemblies of the church, or to study God's word, because they are so focused on the need to work, to make ends meet.