The way singing shatters glass is through the frequencies which resonate with the glass and displace air particles.
When those frequencies or sound waves from the singers voice resonates with the glass and basically does what is known as an invisible force against the glass it shatters because it cannot stand up to the frequencies and force of the sound waves.
To break most glass by singing you need to sing at a frequency of above Octave Middle C.
The actual frequency at which you need to sing to break glass with your voice depends on the type of glass and how thick or thin the glass is.
Thicker glass will require a higher note of singing while thinner glass can be shattered with lower frequencies.
You can really break glass by singing.
However to be able to break glass by singing you need to have a highly trained person who has a good singing voice.
It takes some talent to get good enough at singing at a high enough pitch to actually break glass.
I watched an Opera Singer do the breaking of glass at an event at a fair before and yes it's possible for them to break the glass.
Breaking glass or shattering glass with your voice by singing is not the easiest thing to do because to break glass or shatter glass with your voice it requires singing at precisely the pitch at which a particular glass resonates and with enough decibels to shatter the glass.