I am the bread of life; whoever comes to me will never hunger, and whoever believes in me will never thirst. In response to the crowd’s request for the life-giving bread that he had “dangled” before their very eyes (Sir, give us that bread always [cf. John 6:34, yesterday’s Gospel reading]), Jesus reveals that he indeed is the bread of life. It was not the response that had been expected and as such was not wholeheartedly received by those who had put forth the inquiry. As a matter of fact, as we will see later on, it made the crowd to begin doubting the sanity of Jesus. Jesus was aware of this, and he proceeded to address it as well.  
Bread symbolizes nourishment. It symbolizes that which is not only basic but necessary for life. In other words, bread symbolizes life. And so when Jesus promised the bread of life, the crowd understood it to mean exactly that: the bread that they needed in order to live. When Jesus promised them life-giving bread, they understood him as talking about their daily nourishment (cf. John 6:34: “give us this bread always so that we do not have to hunger again!”)
Jesus knew the importance of meeting the needs of physical nourishment and understood it as part of his mission. Providing that which is necessary for physical nourishment was an unmistakable sign of Jesus’ messianic mission (otherwise he wouldn’t have had pity on the crowd and provided bread for them). However, he did not want the people to see him only in terms of meeting their physical needs. He wanted them to see in him an opportunity to regain that which they had lost on account of their rebellion: eternal life. Jesus as the bread of life meets the most essential needs of the human person: a life with God. Jesus as the Word of God made flesh becomes the source and sole means of attaining the fullness of life with God: this is the will of my Father, that everyone who sees the Son and believes in him may have eternal life, and I shall raise him on the last day.