The Psalmist reminds us that if we are wiling to submit ourselves to God, then God will sustain and support us. It is wonderful to know that God cares and He is always there on our behalf. Back in verse 10, we saw the fact that all people will one day acknowledge God. Some will praise Him by force and some out of free will. It is much more blessed to willingly submit to Him in this life in order for Him to use us for His divine glory and honor in today and in the future.
 The eyes of all wait upon thee; and thou givest them their meat in due season.  Thou openest thine hand, and satisfiest the desire of every living thing.
This Psalm likes to go back and forth between focusing on God's relationship with believers and His relationship with the whole world. These two verses come back to God's relationship with the whole world.
So how does God give all of us food at the proper time? We have a general principal here and David is not talking about every specific person in history. The point is, God provides an environment where food can grow out of the ground and animals that that can be killed for food. To quote an old Jewish expression, "The greatest purpose that an animal can serve is as food for humans." David's point in these verses is simply that God has provided for us an environment where we do have food we can grow and eat. This is all due to God's provision.