One Explanation of This custom dates back to Talmudic times, and symbolizes the idea of our keeping Jerusalem and Israel in our minds even at times of our joy. Just as the Temple in Jerusalem is destroyed, so we break a utensil to show our identification with the sorrow of Jewish exile. The verse, "If I forget thee O' Jerusalem, let my right hand forget its cunning: If I do not raise thee over my own joy, let my tongue cleave to the roof of my mouth", is sometimes recited at this point. 

Another follows the custom of lovers throwing their glasses into a fireplace.  Once they have tasted of the glasses, destroying them prevents any other from partaking, thereby preserving their exclusive and sanctified relationship.

With the breaking of the glass music plays, and the guests usually break out into dancing and cries of "Mazaltov! Mazaltov!" (Some say, tongue in cheek, that this moment symbolizes the last time the groom gets to "put his foot down")

Extra: Bob has chosen to place his glass into a satin bag that he personally sewed for his guitar accessories almost 30 years ago.