The meaning becomes clear when you take the Last Supper in its Jewish context. Jesus is performing a Seder meal. In the Seder meal, the historical event of the Passover is literally "made present;" it is more than a simple re-enactment.
Also, to complete the Seder meal, it was necessary that the lamb be entirely consumed.
I found this interesting link showing how the Seder meal reveals Christ
Thank you for the interesting link. I've printed it out, so that I can keep the refs handy.
However, two things still stand out to me. Nothing there to my eyes makes a case for dogmatic transubstantiation. Paul is clear that the meal is about vastly more than food, and I think all Christians understand that. I just don't see any Scriptural (or extra-Scriptural) imperative to engage in pseudo-mystical mumbo jumbo that has no concrete sense.
FWIW, one thing that gets completely lost in Catholic mass (and Protestant services) is the notion that the Lord's Supper was, in fact, a meal. This seems perfectly clear in Scripture and out of it. The Lord's Supper as practiced by original Christians was an extended gathering of people for a meal, where people sat around, talked, exchanged views, and shared the time with each other while eating with the understanding that it was a meal and time and experience dedicated to Christ Jesus...
Religious services nowadays have replaced this meal concept and engaged interactivity dedicated to Jesus with ritual and "guided" imagery...
Mark W.