Following the feeding of the 5000 (the only miracle of Jesus recorded in all 4 of the Gospels) and Jesus walking on the water, we come to the extended "Bread of Life" teaching. Jesus is clearly speaking in Eucharistic terms when he speaks of eating his body and drinking his blood. His listeners think he has gone completely mad and is inviting them to participate in some cannibalistic ritual. In the early years of the Christian movement (at least into the 4th century) one of the accusations against the Christian movement was that the Christians got together and ate children. The religious people do not understand what he is talking about and, frankly the language Jesus uses: referring to himself as Manna, calling himself "living bread", etc. does not leave much room for a broader understanding. Without knowledge of the Lord's supper his listeners would be clueless.
The best exchange in the passage comes at the end. Because of this teaching many of his disciples left him (verse 66) and when Jesus confronts the 12 (and the inner circle) and asks them: "do you also wish to go away?" (verse 67) Simon Peter, speaking for the group, says: "Lord, to whom can we go? You have the words of eternal life!" Often times Jesus expects certain attitudes, certain beliefs, certain behaviors that run contrary to the world around us. There have been times in my life when following Jesus has been difficult and being faithful to his call on my life nigh unto impossible. . . in these difficult times I remember when he claimed my life, and called me out of darkness. Every time I remember that he has the words to eternal life and I push on.