First of all, it may be the nervousness and inadaptability caused by emotional excitement that led to the accidental breaking of the glass.
Secondly, it may involve some ceremonies or procedures at the wedding, and it may involve the custom of throwing things, so as to indicate that the new couple can break the old shackles and welcome a new life in the future.
Finally, broken glass may also represent a psychological change, that is, the groom has changed from single to married and is willing to change his mind for the bride.
The above is just speculation, and the specific answer may vary according to the region, culture and personal situation.