Audio amplifiers often use negative feedback to correct errors in the output signal. The output signal is compared to the input signal and the differences are fed back into the input to correct the error. If the signal is low enough in frequency and the feedback loop is fast enough, the error is summed to the original signal out of phase and the error is corrected in real time.
If the feedback loop is too slow or the signal is too high in frequency, then the error can be fed back incorrectly such that the error is actually amplified further and the circuit oscillates at some resonant frequency, similar to what you get when you point a microphone at a loudspeaker driven by the microphone's output. The howl, make it stop!
What was happening in the linked article was that the feedback loop of the amplifier being tested was responding to some inaudible frequency that appeared on the speaker cables, apparently due to some radio transmitter nearby. The feedback loop was not designed to correct for frequencies in this range, and the amplifier began to oscillate. The loudspeakers presented a very high impedance at the oscillation frequency, and so most of the power generated was dissipated in the output transistors, heating them to the point that the protection circuitry kicked in.
The zobel that they added presents a low impedance to the amp for high frequency signals. High frequency energy is dissipated in the zobel's resistor, preventing the oscillation from starting.
Adding a zobel is a safe thing to do for any amplifier. Many loudspeaker crossover networks include one, but many don't.
