One reason is in order to remember the Temple and the glory of Jerusalem during that era as it says in the verse in Psalm 137:
If I forget you, O Jerusalem, let my right hand forget its skill. Let my tongue adhere to my palate if I fail to recall you, if I fail to elevate Jerusalem above my foremost joy.
So even at a time of "foremost joy," we smash a glass in order to remember the destruction of the Temple.
Another reason is based on the Talmud in Tractate Berachot:
"The Torah says 'Serve God with awe and rejoice with trembling'... Rav Ashi made a wedding for his son. When he saw that the Rabbis were getting 'carried away' in their rejoicing, he brought out a crystal glass and broke it before them and they became subdued."
Many commentaries state that this is the source for the breaking of the glass at weddings. We learn from this that even at an occasion of great rejoicing, one must take measures to ensure that the celebration remains within bounds of propriety.
