Yes, they are the fruits of a potato. The two plants (tomato & potato) are closely related members of the Nightshade family. Also, like most members of that family, the fruits are poisonous.

As Ilex says these are the fruits what you dig up is a root enlargement. Just make sure to bin all the potato top a root that you dig up - don't compost.

take it easy folks.A potato is a tuber.It never grows in mid air.A tomato
is not a tuber.So this will have to be one or the other.From what I see
in the picture it is not a potato nor a tomato but defenitaly not both.

Guest is growing potatoes so the photo shows the 'fruit', which on a potato is poisonous. The part of the potato which we eat is a 'tuber' this is specialized plant part (subterranean stem) known as stolon. This means that, in a strict botanical sense, it is a modified stem. So no it isn't a root enlargement.

When Guest lifts his/her potatoes they need to either burn or bin all the foliage and the remaining roots. The reason for doing this is to ensure that no blight spores get into your compost.

Easyman - I think perhaps I could have phrased my initial answer more carefully!

I didn't mean to suggest that tomatoes are the fruits of a potato plant, but rather that the picture shows the fruits of a potato plant, and that the Tomato (Solanum lycopersicum) and the Potato (Solanum tuberosum) are very closely related plants which explains why the fruits of a potato plant do indeed resemble small tomatoes.....