This one is a miniaturized version of Gyraf's High Power Headphone Amp.
It's basically an opamp with boots on, as they say, which is a definition easily expanded to include the whole lot of power amplifiers out there. In a quick look at any opamp's datasheet and the nightmare of transistors they contain, you can segment them up into the three-stage design found in the overwhelming majority of linear amplifiers out there: Input differential transconductance stage, Voltage Amplifier Stage and then some form of unity gain output amplifier that acts as a (hopefully) ideal voltage source to power the loudspeakers.
Here you can experience that in mini, with some LEDs added as the diode drops to steer the bases of the output transistors, creating the micropower variety of what can be found in much larger designs as well, for example, the legendary standard ART SLA-1 studio amplifier, which is essentially the gorgon equivalent of this little thing here.
The opamp handles input and gain staging, and produces a push-pull output signal that is then applied to however powerful output transistors you like and can keep stable, with global feedback going back into the opamp's input.
A great learning piece, and a super fun accessory you can cram into pretty much whatever design you're building.