Psalm 81:10 "I am the LORD thy God, which brought thee out of the land of Egypt. open thy mouth wide, and I will fill it." (KJV)
What was the land of Egypt for the Israelites? See Exodus 20:2 It was the house of bondage(land of bondage) in those days.The mouth speaks of eating or being fed. It is a part of our physical bodies. But, the Lord God was using this analogy to describe the inward hunger of man(and women): of the desires of man, and that which feeds the part of a man's soul.
If you read further in Psalm 81, you will find out how they were satisfying their hunger. Read the entire Psalm to understand the Words of God.
What does man seek after(hunger after)? After the praises of man, or of God his maker? Does man seek after that which will bring him satisfaction; money, possessions, fame, or standing in life? Or does he seek after the counsel and provision of His Maker?
King David said in the Psalm 71:8, "Let my mouth be filled with Thy praise, and with Thy honor all the days."(KJV)
Also read:
Psalm 126:1-3, Proverbs 18:20-21 KJV