What does "broken for you" mean or imply?

I recently spoke on the Last Supper and how Jesus took the Passover feast and showed the disciples how He wanted them to remember His work on Calvary. In Paul’s letter to the Corinthian church (I Corinthians 11) he records how Jesus took the crispy flatbread, broke it, and said words to the effect, “Take it, eat it, this is my body which is ‘broken’ for you, and do this to remember me.” The Old Testament is clear that at the sacrifice of the Messiah for sin no bones would be broken. So, what does “broken for you” mean? I do recognize that earlier manuscripts do not have the word “broken.”