This phrase is recorded 4 times in the New Testament. Here's the basic scene:
Jesus and his disciples are sitting in the upper room, on the eve of his betrayal and handing over to roman officials. It is also the time of passover. Like the passover lamb of the exodus story, Jesus is telling His disciples, later to be the apostles, that He is going to die and through the shedding of His blood, he will save them from death. (let's stop a minute and get saved here.)
So he breaks the bread and passes it around to them. Now, here is the picture. Jesus Christ took what most believe to be a single piece of bread and broke it. This is obviously important, because there is still only one true way to heaven, and it is sealed in the blood of Christ.
However, I do believe there is a deeper imagery that the Lord was also communicating. There now sits twelve men around the table, holding the twelve pieces of the one bread that Jesus broke... and Jesus says, "This is my body." Is it not possible that as the master craftsman and one true head of the church, Jesus was also telling them that His earthly, flesh and bone, body is going to die and decay, but that they... the believers ... are going to be the new body of Christ.
Doesn't this also jive with Paul's later teachings about the body of Christ? Are we are all not members of one body? "Because I am not a hand, I am not a part of the body..."
Whether Jesus Himself communicated this thought that first night in the upper room is not explained in Scripture. But, the words and concept definitely resonate throughout the early disciples and the New Testament church, and still holds true today.
"This is my body" is you, and me, and everyone else who calls Jesus their Lord and Savior. To take a small license with the wording, it might better be stated:
"You are my body"
- Just a thought.