It restores 10 (12 if you have the food sanitizer) of your Hit Points without irradiating you. It is one of the few edible food items that doesn't give you any radiation, besides other fresh fruits or vegetables.
The scientists at Rivet City have a large stock of fresh fruit and vegetables, and will say, "Be careful, that stuff is worth more than you" or "Don't touch the vegetables, they're fragile."
In the Rivet City science lab, one of the potatoes has no owner and can thus be taken without negative Karma. It is on the table with the Bobblehead - Intelligence and is the closest of three potatoes to the test tube racks.
The potatoes are sold to residents of Rivet City.