On the next day, Jesus taught in the synagogue in Capernaum, saying, "I am the Bread of Life" (John 6:32, 35, 48). Though willing to receive the physical bread, many would not receive the living Bread—Jesus Christ who came down from heaven. Thus, the miracle of feeding the multitude was actually a sermon with visual aids.
The main lesson of the miracle is that Christ is the Bread of Life to a dying humanity, and in Him, there is enough to satisfy the entire world. Only He can satisfy the spiritual hunger in mankind. Jesus says, "I am the living bread which came down from heaven. If anyone eats of this bread, he will live forever; and the bread that I shall give is My flesh, which I shall give for the life of the world. . . . Unless you eat the flesh of the Son of man and drink his blood, you have no life in you" (John 6:51, 53). The Bread that is Jesus gives life in the present (John 6:35, 47) and eternal life in the future (John 6:27, 40).
The tragedy is that people waste time and money on "that which is not bread" (Isaiah 55:1-7). Waste is an enemy of miraculous generosity, so great care was taken to collect the leftovers, though we are not told how they were used. The lesson is that overabundance does not justify waste.
We also learn that Christ asks that we give Him all that we have and allow Him to use it as He sees fit. When we do this, we never lose, always ending up with more blessings than when we started.