A Zobel network is based on the image-impedance principle. Their claim to fame is that the input impedance is fixed in the design and is independent of the transfer function.
In general and in simple terms a Zobel network’s function is to help present a constant impedance (in a perfect world they would counteract the reactive component, leaving a purely resistive load).
They were used extensively to widen and flatten the frequency response of copper phone lines.
In our hobby one of their uses is to cancel the reactive component of a loudspeaker driver. This can help maintain constant impedance as seen by the output of the sections of a speaker crossover (in a perfect world this would make the load as seen by the section of the crossover purely resistive) and this will help maintain the design characteristic of the sections of the crossover.
They may also be found on the output of audio amplifiers to help to enhance the stability of the amplifier.
In the broader context a Zobel filter may be designed as a low-pass, high-pass, band-pass or band-stop filter. It may also be designed as a flat frequency response attenuator.
In our hobby the name Zobel in more well known for impedance compensation in loudspeakers, although IIRC, none of his papers or patents referrer to this application.
It is true that not all speaker manufacturers make use of a Zobel network, much in the same manner as they do not all use constant resistive load attenuators (L-pads) in their designs, even though if a potentiometer is use, when the amount of attenuation is changed, it will shift the crossover point of the crossover section.