Today’s Gospel tells a story from the next day after Jesus had fed the five thousand with the five loaves. In St. John’s account of that day he wrote that the crowd, in becoming aware of the great miracle happening before them, began saying, “This is truly the Prophet, the one who is to come into the world.”
They were referring to Deuteronomy, 18:15 where Moses had promised that at some future date God would raise up a Pophet like himself to whom they would need listen. When the people then made a move to make Jesus their king, he slipped away from them. On the following day when they caught up with Jesus across the lake in Capernaum, they wanted to know if he really were the Prophet whom Moses had promised centuries before.
Now, it had become a belief among the people that when the promised Prophet came, he too would bring down manna from heaven. To check if Jesus were that Prophet, they asked him what sign he could give that would be like Moses bringing down bread from heaven, and Jesus told them that what Moses gave them was not true bread from heaven.
It is possible that Jesus based that answer on the historical fact that what their ancestors took to be bread from heaven was actually a bread-like substance that can still be found in the Sinai Desert. There are aphids feeding on shrubs there that exude a white, honey-like, substance that the Bedouins still call “manna.” Like the Bible manna, it must be gathered in the morning, because at 80 degrees it melts into the sand.
At the beginning of his long discourse on the Bread of Life Jesus then said that he was the true bread from heaven. Later in the discourse he would describe himself as the bread we eat in Holy Communion, but at the beginning he was saying that through his teaching he was the true bread which we must believe in for the nourishment of our souls.