Hmmm. i see this often in eBay auctions... did it come in that wooden box in the background?... also is it about 6" x 2" (15cm x 5cm for my metric friends).
If the above is correct then I suspect it's a Norton India Oil stone as mentioned by FiveOhNine... and some of the ancient oil has dried up on the surface.
If it is the oil stone, then when you lap it the fine side will appear pink or deep peach color, Also, it may or may not have the inked stamp on the side or it may be faded.
The unfortunate thing is... they are sometimes unevenly joined like a natural coticule/bbw combo stone, and because of the pink color, when photoed by an amateur, looks just like a cotocule.
But you are not alone... I have one too.
However I could be wrong... and you may may be lucky, and have a Frictionite type hone that simply needs a little cleaning or lapping.
Give the thing a lapping, if it's so hard that you feel a few "new" muscles developing on your arm, then you may have a Norton... however, if it laps easy, then you may have one of the most valuable vintage man-made razor hones in existence.
Please let us know how this works out.