"Squeeze Box" is a slang term for an accordion, but it is also slang for the vagina. The band just wanted to see if they could get away with singing about the joys of explicit sex.
In the liner notes to Pete Townshend's compilation album Scoop, he wrote that he recorded the song for fun one day when he had bought himself an accordion. The accordion gave the song a polka-esque rhythm and the lyrics were "intended as a poorly aimed dirty joke." Townshend had no thought of it ever becoming a hit.
The song is about an accordion (sort of), but there is hardly any of the instrument in the song. You can hear some in the section about 90 seconds in that goes, "squeeze me, come on and squeeze me," but the subsequent instrumental section is mostly banjo. Pete Townshend played both instruments.
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