Those are NOT potatoes. They are seeds, seed pods. They are NOT edible and would make you very ill if you did. They are a normal result of potatoes blooming and being pollinated. They are not related to the below ground production.

And blooming may or may not be an indicator of below-ground production. That depends on the variety, the age of the plants, and several other factors.

With some varieties of potatoes you will never see blooms. With others the sign of blooms can indicate the small new potatoes are developing below ground and some folks will carefully dig into the side of the plant hill and harvest those. Most prefer to let the crop continue so that you can harvest full size potatoes once the tops die off.

Dave

Sorry forgot to add that you really need to remove those seed pods and toss them. Best for the plant and saves you having all those tiny little seeds sprouting in the garden next year.

Dave

Yeah, potatoes are tubers, modified roots. Potatoes are in the same general family as tomatoes and peppers, so they do have "fruit". However, its also in the same family as Deadly Nightshade and the berries produced by a potato plant can be lethally toxic.

You've got two options:
1) Let it make fruit and save the seeds. Yes, potatoes do grow from normal seeds just like any other plant, its just that the tubers that form from those plants tend to be small. Usually when a farmer sows direct seeds like that they use the tubers it develops as the next season's seed potatoes.

2) Pick them off now to get bigger potatoes underground. It stops the plant from putting energy into the fruit and makes it think it has to save that energy for next year, aka store it in the tubers.