Staining (spots, anything visible) can be either metals (mineral) or organic.
If they are organic, most always they are removed or lightened noticeably with a chlorine tablet placed on the for a few minutes.
If they are metal , (inorganic) they can usually be lightened noticeably by crushing up some Vitamin C tablets and putting them in a sock or nylon then holding it directly on the stain for five minutes or maybe more.
I suspect they are inorganic from the looks of the spot you posted.
Other possibility is simply dark colored stone that used to have a very thin layer of plaster covering it and now that very thin layer has worn off.
If they are organic, most always they are removed or lightened noticeably with a chlorine tablet placed on the for a few minutes.
If they are metal , (inorganic) they can usually be lightened noticeably by crushing up some Vitamin C tablets and putting them in a sock or nylon then holding it directly on the stain for five minutes or maybe more.
I suspect they are inorganic from the looks of the spot you posted.
Other possibility is simply dark colored stone that used to have a very thin layer of plaster covering it and now that very thin layer has worn off.