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 previous day he wrote that the crowd, in becoming aware of the great miracle happening before them, had begun 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 Prophet like himself to whom they would need listen. When the people made a move to make Jesus their king, he slipped away from them. On the following day when they caught up with him 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 desert shrubs, exuding a white, honey-like, substance that the Bedouins still call “manna.” Like the Bible’s manna, it must be gathered in the morning, because at 80 degrees it melts into the sand.
Later in this discourse from Chapter Six of John’s Gospel, Jesus would turn most of his followers away by insisting that the Bread he would give them to eat was his flesh. But here at the beginning of the long discourse, he seemed to be saying that his teaching was bread for their souls that they would need to believe to have life in them.