Ground switches and "death caps"
This is probably more than you ever wanted to know about ground switches and "death caps"...
In the US, conventional power outlets have one side of the line at ground potential and the other side connected to the "hot" lead. The ground switch works by creating a high-impedance connection, through the grounding or "death" capacitor, between the chassis and one side of the AC line. The "correct" connection attaches the capacitor to the grounded side of the AC line, thus putting the chassis at ground potential for AC frequencies.
The cap really was necessary; without it, leakage currents (mostly from the power transformer) would put some small amount of AC voltage on the chassis. With the entire circuit floating up and down on the AC voltage, a certain amount of imbalanced voltage would get injected into the circuit and cause hum. The cap simply shunted the chassis voltage to ground, greatly reducing the magnitude of the voltage and reducing hum.
The ground switch itself was a convenience. Most products of the era had the cap without the switch; you'd have to reverse the AC plug in the outlet to get the proper connection.
All this came about because grounded outlets, although available, were not required by the electrical code until sometime in the `70s, I think. Grounded outlets were preceded by polarized outlets which had one prong wider than the other. A matching polarized plug could only be inserted one way. For backward compatibility, a non-polarized plug could be inserted either way. Before that, of course, both plugs and outlets were non-polarized (and ungrounded). Now that we have grounded outlets almost everywhere, the function of the ground cap has been replaced by a direct connection from the chassis to the safety ground through the round pin of a 3-wire plug.
The "death cap" appellation is fairly recent. My cynical side says that the name was probably invented to drum up business for amp techs... The name is appropriate, even if it does overstate its case. What can happen is that the capacitor can fail shorted which allows it to pass DC. That's like wiring the chassis directly to the AC line, which is a lot like sticking a finger into one side of the AC outlet; you have a 50/50 chance of getting zapped.
The cap may fail shorted due to manufacturing defect (rare) or dielectric punch-through. A capacitor is made of two strips of metal separated by an insulator, or dielectric. The dielectric is rated to withstand a certain amount of voltage. Higher voltages may breach the dielectric. The grounding cap is subjected to line voltage when not properly connected (switch or plug in the wrong position). Line voltage is nominally 120 volts AC (now; it has crept up by a few percent over the decades) and a properly-manufactured and rated cap will tolerate that for many, many decades. However, AC line voltage is not "clean"; it's host to much higher spike voltages that happen when motors get switched off or when there's a nearby lightning strike. A high-voltage spike can punch through a weak spot in the dielectric material, burning a tiny permanent hole and - via carbonization or welding of the electrodes - create a DC path through the capacitor.
Now, getting zapped with the full 120 volts is unpleasant (I can vouch for that) but not universally fatal (ditto). It happened a lot in the days when vacuum tubes could be purchased at the corner store, and very few people died from the experience. Guitarists, though, are at greater risk than the general public because they have a firm grip on a piece of metal connnected to the chassis. If that grounding cap fails shorted and the grounding switch (or plug) is set wrong, the unlucky guitarist is going to be connected to the AC line. Assuming that the guitarist is wearing non-conductive shoes and not touching anything else, he'll notice a buzzing sensation which may range from noticeable to somewhat unpleasant. At that point, touching any grounded piece of metal - say a microphone - completes the path. If the path of the electricity through the guitarist's body happens to involve the heart, we end up with a "late, as in departed" (gratuitous Douglas Adams quote), guitarist.
I developed a set of habits which have protected me from getting zapped. I always wear non-conductive shoes, use one hand to turn on an amp (with the other hand not touching any metal), and run a knuckle across the faceplate to see whether there's any buzzing sensation. The knuckle test, for some reason, is more sensitive than just touching the amp and is safer because you don't have a grip on anything.
On a closing note, let me add that a three-wire cord provides no guarantee of electrical safety. It's possible to encounter a miswired outlet which can either leave the ground floating or - even worse - connect the safety ground to a voltage source. Get one of those three-light grounded-outlet testers and use it before you plug in your amp at an unfamiliar venue. And if you'll be touching any gear other than your own rig, give it a "preflight" check using the knuckle test.