An apparently common nickname for an accordion. I had never heard this term before, but The Who wrote a song about it (called "Squeeze Box", interestingly enough). Part of the lyrics are below:

Mama's got a squeeze box
She wears on her chest
And when Daddy comes home
He never gets no rest

'Cause she's playing all night
And the music's all right
Mama's got a squeeze box
Daddy never sleeps at night

When I first heard this song, I had no idea what the hell a squeeze box was. For some reason I imagined it to be some sort of device that made this woman extra horny, thus keeping her husband up all night.

Yes, I'm stupid...