In Jewish tradition, what is the symbolism regarding breaking the glass after the wine is shared?

It has a variety of symbolisms. It reminds us that, even in happy times, we are to remember the destruction of the Temple in Jerusalem by the Romans. Another is the hope that the bond of marriage be as difficult to break as it would be to piece together the broken glass. A third is a symbolic representation of the loss of the woman's virginity (I'm sure you can fill in the details). There are other meanings; see also the links below.

Thank you, Mark S. very interesting and informative answer.