This is a treadle scroll saw. Yours looks a lot like my Rogers. The deep throat made it possible to cut designs into the interior of a larger board rather than to simply cut decorative cuts or to cut out figures of one sort or another.
The blade could be detached so that it could enter a hole drilled into the wood. I can't see it from the picture, but these often had a small drill chuck mounted on the side for making the holes to slip the blade through.