This verse is found in John Chapter 6. The entire chapter should be read for context as well as cross referencing other passages. We call it different things like Communion, the Eucharist, or the Breaking of Bread. Various denominations and even individuals have different views on what this means. Is it literal or spiritual in meaning? Is this the literal body and blood of Christ or is it done in remembrance and figurative? For me, the answer is quite simple and found in the context itself.
The question in this passage will boil down to a literal versus a spiritual understanding of what Jesus is saying. The answer is found in John Chapter 6:
63The Spirit gives life; the flesh counts for nothing. The words I have spoken to you—they are full of the Spirit e and life. 64Yet there are some of you who do not believe.” For Jesus had known from the beginning which of them did not believe and who would betray him. 65He went on to say, “This is why I told you that no one can come to me unless the Father has enabled them.”
That is the short answer and should suffice for most people. Jesus is not speaking literally and even says “flesh counts for nothing.” He adds the reason some turned away from this saying. “no one can come to me unless the Father has enabled them.” That is why many turned away. The Father had not enabled them, which is another lengthy and contentious discussion among men.
Other passages to consider
John Chapter 4 contains the story of the Samaritan woman at the well. Jesus told the woman:
“Everyone who drinks this water will be thirsty again, 14but whoever drinks the water I give them will never thirst. Indeed, the water I give them will become in them a spring of water welling up to eternal life.”
Jesus obviously means this in a spiritual sense as He did in John Chapter 6.
The Last Supper is contained in Matthew 26:17–29, Mark 14:12–25, Luke 22:7–38, and later Paul discusses it in I Corinthians 11:23–25. Luke is the only Gospel that includes “do this in remembrance of me”. If we were only to have Matthew and Mark it would simply be a story and not a practice of the church today. The Biblical reason we practice it today is based on Paul in I Corinthians. Otherwise, people could easily draw the conclusion that Jesus was only speaking to the disciples.