It's a rather long and interested discussion as New Testament discussions go.
One thing I recently learned was that the Jews of that era had a traditional belief that, just as the great prophet Moses had given the people manna, "the bread of God", so would the great Messiah, when he came, give the people "the bread of God" as well. So that's likely why, with the bread of the day before and the hope for a looked-for manna-bearing Messiah, they bring up the story of the manna which leads, in turn, to the discussion of the bread of life.
Jesus says in this chapter that just as God had sent manna (the bread of God) in Moses' time to sustain the mortal life his people, so has he sent the bread of God (manna) in the time of the Messiah to sustain the everlasting life of his people. And that bread is him.
Now, it's interesting to me how the various people in this episode respond. But first, it's important to note that all of the people in this scene are people who have come to listen to Jesus. Some of them came in the boat with him. Some made the long journey across the water to get to where he was once they figured out that he'd left. Others were already living on this side of the lake and had come to listen. All of them were interested in hearing what he had to say, either having already decided to follow him or trying to figure out if they should or wished to follow him. They were a community of seekers.
Like, you might say, the congregation I attend, and, if you attend a congregation, probably like yours as well.
As the conversation continues there are a number of reactions. There are some who don't get it because they don't understand Jesus' meaning. (vs. 41-42) There are some who just don't believe him on this particular teaching but are willing to stay and keep discussing.. (vs. 64). There are some who don't understand him and think what he's saying is too much and leave, at least for now. (vs. 66) There are some who think they get it, at least the part about him being the Christ, though we know that there is much that they have yet to learn (vs.67-69). And there are some who just don't get it at all, have potential to cause harm, and don't leave. (vs. 70-71)
I'm betting that in your congregation, like mine, there are corresponding individuals as well (as well as other situations of being that are not in the above list).
Jesus engages all of them in the conversation instead of dividing and creating separate groups to talk with. He's willing to address and interact with a community of seekers that involves various levels of comprehension. And so the ones who stay as part of that conversation are a very diverse bunch in terms of their comprehension and understanding.
So I think about myself and the community of seekers I worship with. What do I learn?
I learn that in the eyes of Jesus, we are seen as a community and that he teaches all of us together, regardless the current status of our comprehension or faith.
I learn that there will be people in my congregation who understand Jesus' message the way I do, and, because our particular congregation is organized by geographic location and is not self-selected due to our having similar understandings there will plenty who understand and apply Jesus' message differently; some who understand it better than I do, and some who find it more confusing than I do, and some who really are missing the major points and have potential to do serious harm. Though Jesus hopes we will eventually all become one as he is one with the Father (John 15) he understands that that happens one person at a time and so he doesn't require that all of his disciples be at a similar level of understanding at the same time, or even progressing, in order to be part of the community..
Thinking about the trajectory of belief that Peter will undergo as the story continues, I learn that I and every other well meaning disciple still have much learning to do.
And, by extrapolation, if we all in that community are either learning good or heading treacherously towards dangerous error or muttering about what we don't yet understand, or feeling confused by what we've heard, or any combination of the above, then we are all, personally, in a state of flux. Which means that we, as a congregation or community of seekers, will never, at least in this life, all be at the same level of understanding at the same time. And Jesus understands that.
And that last paragraph is good for us to know.