I'm 48, my parents absolutely grew up through rationing which lasted into the 1950s. Plain boiled potatoes was a really common way of serving them all through my childhood. Even now they will commonly eat plain potatoes, with a bit of butter on them. In fact as they have got older, now in their 80s, their meal might just be plain potatoes and peas.
This dish, mince and tatties, was an absolute staple at my Scottish grannie's house, with an overboiled cabbage as well for good measure.
Is that what it means? Ha, I always assumed that was a thickener or something.