Potato cooker is what it is. It is roughly a triangle with rounded sides. The lid is slightly domed and has a glass knob. There is a place at the back that looks like it used to be where the handle connected, but that was long ago.
To 'bake' the potatoes, you wash off baking potatoes, pierce the skins a couple of time with the point of a sharp knife, then fit them into the potato cooker (it holds up to 4 large ones), put it on the stove top with the heat at low and cook for about 45 minutes. The potatoes come out with fluffy interiors and crisp skins as if you had baked them in the oven, but the energy use is far less. We've also baked yams in it and they are wonderful cooked that way.
I'll bet that you could also pop corn and cook rice in this pot, but have never tried it.
Thanks for the great guesses. If you ever see one of these for sale at a yard sale or antiques place, snap it up if it isn't too expensive. I'd love to know what it cost and what they said it was for, too.