John 6:51-58 is so structured that verses 51 and 58 form an inclusion over the whole discourse. This means that verses 52-57 have to be understood within the main assertion of Jesus that He is the living Bread and that whoever eats this bread will live forever. Below is a picture of the text of the New American Bible illustrating the structure of the text. Clicking on the image will show the whole image.
The theme of the murmurring of the Jews continues in verse 52 as they ask "How can this man give us his flesh to eat." Later on Pilate will point to Jesus saying "Behold the Man!" The bloodied and torn flesh of Jesus -- He whose crime will be posted on the cross as "Jesus of Nazareth King of the Jews" -- will be shown to the world and be rejected by men.
In verse 53-56, what was referred to as "living bread" becomes "(my) flesh and (my) blood". To eat and to drink are the basic ways through which human beings and animals draw life. On one level, Jesus drawing attention to the sacrifice he is about to make -- a sacrifice where he will shed his blood and allow his flesh to be mangled and torn. On a higher level, he is saying that in a mysterious way, he will himself be the source of life for all, as their food and drink. "For my flesh is true food; and my blood is true drink."
The word "life" is mentioned 5 times. In verse 51, Jesus declares that the bread he gives, his own flesh, is for the life of the world. In the Gospel of John, "world" can also mean whole of humanity: "For God so loved the world that He gave US His only Son, so that whoever believes in Him may have life." (John 3:16) From a general mention of humanity (=world), Jesus directs his statement to YOU (v.53) (plural, second person). This is not only the Jews who are his interlocutors, or the disciples who are in the background, but also to those who are listening to the Gospel being read. The invitation to eat of his flesh and drink of his blood is directed to specific persons, not to an anonymous "generality." The mention of "life" in v. 53 is in a negative statement which in essence corresponds to v. 58 "Unlike your ancestors who ate and still died..." Those who reject the offer of Jesus, the Living Bread, will themselves be like the Israelites in the desert: they will die. In verse 57, Jesus explains how he will give eternal life (cf. v. 54). Since he lives in the Father, those who feed from him will draw life from the Father Himself. The believer then will share in the life of the Father and the Son. For the moment, this is as far as John 6 allows us to go. The Paraclete will still be mentioned at a later section of the Gospel. In John 14-16, a share in the life of God -- Father, Son and Holy Spirit -- becomes the inheritance of the disciple.
Verse 54 echoes John 11 which involves a good friend of Jesus. Lazarus was a good friend, and therefore, one who shared the table with Jesus. He dies and Jesus raises him up. Jesus presents himself during this event as "The Resurrection and the Life" -- in Him all who have died will live again. Lazarus is a type of the Christian who, in the company of the Lord, does not really die; he lives by the word of the Lord and by the gracious gift of the Father.
Finally, in verse 55, we find an echo of John 15's key phrase "remain in me.". In John 15:1-11 Jesus describes his relationship with the disciples as a vital relationship, as vital as that of the branches to the vine. Understood from the perspective of John 6, this relationship only further highlights the need for the Living Bread which is "real food and real drink."
John 6:51-58 contains the sacramental theme of the Johanine Discourse on the Bread of Life. In the Eucharist, we are given the opportunity to eat and drink of the Bread of Life which is Jesus Himself. The discourse has been composed in such a way that it echoes other sections in the Gospel that contain references to the Passion of Jesus ("Behold the Man"), to Jesus as the Resurrection and the Life and to the special relationship that Jesus has with his disciples. In other words, through the Eucharist, we partake of the life that Jesus has won for us in the Paschal Mystery and each time we partake of it, we are "sacramentally" united to Jesus, as branches to the vine.