A push-pull output stage needs two copies of the signal exactly out of phase with each other — one to push each side of the push-pull pair. The long-tailed pair produces them with two triodes that share a single large "tail" resistor at their joined cathodes. Signal drives one grid; the shared tail forces the second triode to mirror it in antiphase, so the two plates swing equal and opposite. It is a differential amplifier borrowed from instrumentation, and it splits phase while also adding gain.
Designers reached for it whenever an amp had to drive a real output stage hard. Unlike the single-tube alternatives it delivers voltage gain as well as a phase split, its two sides stay closely balanced as the amp is pushed, and it presents a low, symmetric drive to both output tubes — exactly what a 22 W to 50 W stage wants. It is also the natural place to close the negative-feedback loop, injected into the second grid. Once Fender and Marshall standardised on it in the late tweed and blackface eras, it became the default for everything bigger than a student amp.
Sonically that shows up as clean headroom and a firm, symmetric breakup: the sound of a big amp holding together where a simpler splitter would already be folding. For the contrast, the archive keeps both simpler splitters — the cathodyne, which splits phase with no gain, and the single-ended small amps that need no splitter at all.