1 Cor 11:24 in the ESV reads, “and when he had given thanks, he broke (εκλασεν) it, and said, ‘This is my body which is for you (το υπερ υμων). Do this in remembrance of me.’” The interesting phrase is, “which is for you.”
The article το is telling you that the following prepositional phrase is functioning in some substantive manner that is qualifying the previous noun. Jesus says that the bread of communion is “my body,” and in some way his body is “on behalf of you.”
This is typical Greek in that you have to supply a verb; you can’t translate word for word: “This is my body the on behalf of you.”
When you have to supply the verb, the most likely candidate is some form of the verb “to be,” which is what the ESV is doing. The second most likely candidate is some verb previously and recently used in the context. This is what the KJV appears to do with “broken” when it translates, “this is my body, which is broken for you.” It appears to be supplying “broken” from the previous “he broke it.”
But wait; there’s more!