Singing boxes, never given a proper name, are minor characters from the musical Avenue Q. They only appear as backing vocals in the song Purpose. As their name implies, they are six singing boxes with faces.
The faces of the boxes are not seen in the scene leading up to Purpose. They are just moving boxes stacked in Princeton's apartment. As the song goes on, the boxes turn around revealing their faces and moving mouths.
They are puppeteered by the puppeteers of Kate Monster/Lucy the Slut, Mrs. Thistletwat, and Nicky/Trekkie Monster. (In the original cast, Stephanie D'Abruzzo, Jennifer Barnhart, and Rick Lyon, respecitively.)