One word:
induction. When an electromagnetic pulse (EMP) hits, a big magnetic field "sweeps" everything in its path. The moving magnetic field (because it travels out from where it was created) will induce electromotive force (EMF) or voltage, if you prefer, in all kinds of stuff. There are tiny traces on circuit boards, and there are component leads and all kinds of conductors that are acting like little antennas inside electronic equipment. And these little antennae will "receive" the magnetic "signal" from the pulse and convert some of its energy into voltage. Because the pulse is so large, the voltage will be high, and will be high enough to damage components and circuits in all kinds of equipment. This will knock electronic devices out of commission. Permanently.
Shielding is possible, but we can only do a limited amount of that. It's a whole are of investigation, and a lot of it is "top hush" because the applications for the shielding are mostly military. Looked at another way, if an EMP hits because someone set off a nuclear weapon, I'd rather that military aircraft fly and my computer go down than the other way 'round. Certainly the military would, too, and their budget pays for the work.