This quote was in reference to God delivering His people from the land of Egypt. They were completely dependent on Him and He had promised to protect them from their enemies and satisfy their every need. Psalms 81:11 tells us, however, that the people did not listen to God or obey Him. God then says "So I gave them over to the stubbornness of their heart, to walk in their own devices" Psalm 81:12.
Do we not act like this in our lives? God tells us to open our mouths and He will fill them. He tells us to "taste and see that the LORD is good" Psalm 34:8. Peter even refers to this in 1 Peter 2:3. God tells us to depend on Him for He will satisfy the deepest longings of our soul. Why do we go after those things that will not truly satisfy? John Piper has written and preached much about this phenomena. In his book A Hunger for God, he writes the following:
The greatest enemy of hunger for God is not poison but apple pie. It is not the banquet of the wicked that dulls our appetite for heaven, but endless nibbling at the table of the world. . . . The greatest adversary of love to God is not his enemies but his gifts. And the most deadly appetites are not for the poison of evil, but for the simple pleasures of earth. For when these replace an appetite for God himself, the idolatry is scarcely recognizable, and almost incurable.The writes of Hebrews tells us to "lay aside every encumbrance and the sin which so easily entangles us, and let us run with endurance the race that is set before us" Hebrews 12:1. These "encumbrances" are not necessarily wrong in themselves; they just hinder us from running the race. They prevent us from obtaining the best God has for us which is Himself. Let us not allow anything to keep us from the all-satisfying God. Let us pursue and desire God in a way that we have never desired anything else. God is our treasure (Matthew 13:44). God is our pearl of great price (Matthew 13:45-46). As the old chorus goes, "Lord, you are more precious than silver. Lord, You are more costly than gold. Lord, You are more beautiful than diamonds, and nothing I desire compares with You." May that be the prayer of our hearts. God promises that if we open our mouth wide - He will fill it and He will satisfy us with Himself.