It's not as daft an idea as some seem to think.
If a nuclear bomb goes off nearby, it won't do any good - realistically nothing will.
If a nuclear bomb goes off a long way away, you might not get caught up in the initial blast or firestorm that follows. However, you are still at risk of radioactive fallout - the material that gets sucked up into the air following the blast, contaminated with radiation, will come back down to earth over the following hours and days.
Effectively it's just dust, but radioactive dust. It's important to be able to shelter for a few days or couple of weeks as protected from the dust as possible. Either by physical distance or by solid material. A basement is an ideal place to shelter, if you don't have one try to pick a room that's least exposed to the outside and use furniture/books/anything to add material between you and the radioactive fallout.
People seem to think it's a choice between being in a bunker for several years or not taking any steps to protect yourself at all.
Fallout will cause cancer and other illnesses. It doesn't necessarily kill quickly, you might survive several years before it kills you.
Crucially, when the time comes that you wish you had built a shelter, it's probably too late.