It probably helps to redraw the first circuit as an op-amp with +/-2.5V supplies, and treat Vref as GND. Now it's evident the pot is simply a volume control, from IN to GND, with a tap somewhere midway along it. The amp is a regular inverting configuration, gain of 3.
The second circuit is two emitter followers cascaded. This may be pretty obvious, but perhaps why isn't. To be fair, one is probably enough, but two does have the advantage of additional current gain, and canceling out the offset -- the first (TR3) emitter is a Vbe above the input (or say ~3.2V DC), the second is about as much below, or back to ~2.5V. This reduces the "bump" or "pop" at turn-on, through the coupling capacitor. Although, since the headphones aren't grounded to Vref, this is inevitable, but there is still some advantage that the available voltage swing (without clipping/distortion) can be more symmetrical this way.
The ferrite beads help prevent parasitic oscillation (a low impedance applied to an emitter follower can cause it to oscillate, and cables of random lengths can have quite low impedances at "unlucky" frequencies), and also keep external noise/RFI away from the circuit (where it might interfere with the transistors, becoming rectified and now you hear pop-beep-chirp noises in the headphones), and onboard noise away from the headphone cable (an effective antenna).
Tim