Religious Symbolism

The religious symbolism of glass breaking is to remember the destruction of the Jewish temple even in times of celebration and to put Judaism above everything in life. This is supposed to remind the couple of "the psalmist's injunction to set Jerusalem above my highest joy." It is a tradition to recite the entire above psalm.

Romantic Symbolism

When the glass is broken it can never return to how it used to be. This symbolizes the couple's lives changing forever by being married, never to return to their single lives.

Humorous Symbolism

Because it is traditionally the groom who smashes the glass, it is joked that this symbolizes the last time he will ever be able to put his foot down.

Who breaks the glass

Though traditionally it was the groom who broke the glass, some couples choose to break the glass together.

History

According to Rabbi Daniel Gordis, "Most traditional commentators explain this custom as having originated with incidents recorded in the Talmud in which Mar, the son of Ravina, and Rav Ashi deliberately smashed costly glass at their sons' weddings to put a stop to the raucous dancing and celebrating."

Source:

Aish.com: Guide to the Jewish Wedding

Chabad.org: The Breaking of the Glass

MyJewishlearning.com: Nissuin: The Second of the Two Ceremonies: Rabbi Daniel Gordis