Spanokopita . . .
Anyway, I looked for the answer to your question online Angie (I had an idea, but wanted to see what they said). Lots of different answers . . .
I think my gut idea was the most plausible. You party, you drink, you get raucous, you start breaking plates! A mythology has grown up around the custom, and according to sources online it is now banned in Greece because too many people were getting hurt.
The restaurant that used to do it here locally had fake "plates" that were unglazed cheap plaster plates they would use for this. I have to admit, the one time I did it, it was fun, and seemed like the "right" thing to do!