I'll try to explain it as simple as possible :-) ... people that understand EMP may cringe at this analogy :-) ...

EMP is generated when a nuke is detonated in the upper atmosphere ... up in the ionosphere specifically. When this happens, a LOT of electrical disruption occurs. Think of it as a massive, powerful radio transmission across a rather large range of frequencies.

Now, inside any integrated circuit are tiny little metal traces that connect up all of the transistors. Some of these traces can act as an antenna depending on their lengths. So, when this EMP "broadcast" occurs, these tiny antennas can pick up the electromagnetic energy. If too much energy couples onto the antenna, there is a risk of damaging a transistor. It does not matter if the device is powered at the time. In the case of high end CPU, there are millions if not billions of transistors these days ... the probability of one failing if the chip is in the path of an EMP blast is pretty high.

When it comes to cars, EMP won't damage anything mechanical. The electronics in a modern car are a different story. Fuel injection systems are controlled by a computer ... that computer has integrated circuits that might be susceptible to an EMP blast. The reason people are stating that they want a car made before 1979 is that many of those cars have no computer that controls the cars operation. I do know some had some basic electronic "diagnostic ports" (I seem to recall mid 70s VW Beetles and Terrorist Vans had them). Electronics like that could be at risk, but those will not prevent the car from running since the engine is controlled mechanically (i.e. distributor, rotor, carburetor, etc).

There are ways to reduce the probability of catastrophic damage. As many have pointed out, you can shield an electronic device in a faraday cage. Some integrated circuits are fabricated to be hardened to the effects of EMP ... though the enemy only has to dial up the yield of the blast to overcome those protections.

Overall, nobody knows what will happen for sure. Tests have shown that the effects may be overblown. The origin of the blast could be 100km in the atmosphere ... the energy may fall to a low enough level as it approaches the biosphere. Others believe that it will destroy anything with a transistor.

Overall, it isn't a bad idea to shield some electronics just in case of course. The effect isn't all theory ... it can be observed and it is real. I don't think you need to shield your entire home of course, but a little bit of prevention certainly wouldn't hurt (things like a generator would be something to shield since the power grid will fail ... I don't think for long, but long enough to make things interesting to say the least ... also, a backup of any electronic maps, docs, photos, etc wouldn't be a bad idea ... and maybe a cheap laptop or tablet to access them ... obviously print a hardcopy of anything that would be ultra critical).