A fallout shelter was an underground living space built to survive nuclear bombardment.
In one account of the creation of the Daleks, after a meteor strike had destroyed the Humanoid Daleks' stockpile of neutron bombs and irradiated Skaro's atmosphere, Yarvelling and Zolfian hid in a fallout shelter for two years, emerging to discover that their race had mutated into Daleks. (COMIC: Genesis of Evil)
The First Doctor theorised that the Dalek City had originally been a large fallout shelter that had ballooned in size over the centuries since the neutronic war. (TV: The Daleks; AUDIO: Return to Skaro)