"No one can come to Me unless the Father who sent Me draws him and I will raise him up at the last day. It is written in the prophets, 'And they shall all be taught by God.' Therefore everyone who has heard and learned from the Father comes to Me. Not that anyone has seen the Father, except He who is from God; He has seen the Father. Most assuredly, I say to you, he who believes in Me has everlasting life. I am the bread of life. Your fathers ate the manna in the wilderness, and are dead. This is the bread which comes down from heaven. If anyone eats of this bread, he will live forever; and the bread that I shall give is My flesh, which I shall give for the life of the world."
Our Lord taught that the Father must draw an individual to Jesus. However, this is not done in some miraculous, irresistible way but through the word of God as John 6:45 explains - "It is written in the prophets, 'And they shall all be taught by God.' Therefore everyone who has heard and learned from the Father comes to Me" (cf. Isa. 54:13). The law and the prophets, writings which were inspired by God, were designed to bring men to a knowledge of Jesus (cf. Gal. 3:24). All who properly learn of the Father through the Scriptures will come to Christ. Thus, those who are drawn to Jesus by the Father are those who have accepted the teaching of the Scriptures regarding Him (for us today that would include both the Old and New Testaments). The Father had tried to teach these Jews, but they wouldn't learn, just as their ancestors wouldn't learn. In both cases the people were to blame, not God.
"Not that anyone has seen the Father, except He who is from God" (cf. I John 4:12). Jesus didn't want these Jews to conclude that it was necessary to see the Father in order to be taught by Him. Such was not the case. The Father did His teaching through the Scriptures and through the prophets. The fact that Jesus had truly seen the Father and was from God was further testimony to the fact that His teachings should be accepted.
In John 6:47,48, Jesus asserts two primary propositions that He will expand upon in the following verses: (1) "He who believes in Me has everlasting life" and (2) "I am the bread of life."
Although their ancestors had eaten physical bread from heaven (i.e., manna), that bread would not sustain them spiritually. It helped them survive physically as the barley bread had physically satisfied these Jews the day before. However, the true bread from heaven would prevent the eater from dying. Jesus is that bread. To "eat" Him will not prevent physical death, but it will sustain one's spiritual life.
In John 6:51, Jesus combines His thoughts from the prior verses - "I am the living bread which came down from heaven." There appears to be a difference in meaning between the phrase "bread of life" and "living bread." The former refers to that which sustains spiritual life (i.e., Jesus sustains spiritual life) and the latter refers to the fact that the bread itself is alive (i.e., Jesus is alive). In both aspects, manna was inferior bread. It was not alive nor did it have the power to sustain man spiritually.
"If anyone eats of this bread, he will live forever; and the bread that I shall give is My flesh, which I shall give for the life of the world" - Jesus has already stated that to believe in Him would result in everlasting life (cf. 6:47). Now He proclaims the fact that to "eat" of Him (i.e., "this bread") would also result in eternal life. Thus, since the result is the same (i.e., everlasting life) it seems reasonable to conclude that to "eat" of Jesus is just another way of saying that one believes in Him. If one does not believe in Jesus or "eat" of Him, then he will die spiritually even though life was available to him. The same is true in the physical realm. To have access to food for the physical body will do no good if the food is not consumed and digested.
This verse also seems to contain a veiled prophecy regarding Jesus' death. Approximately one year from the time in which He spoke these words, Jesus literally gave His flesh on the cross to make possible the forgiveness of sins for the world (cf. I John 2:2).