Uhhhh.... this is going to be very hard to explain in short terms, especially with my very limited knowledge of the English language ... Anyway, I'll try:
1.) The power supply is very important for any amp. This is simply because there are electronical parts inside the amp, which operate with DC power, so the AC voltage from your local power station has to be transformed and converted to DC. Extremely important is a good filtering stage so that you do not get any influences from the "outside", e.g. other electrical stuff in your household, that could disturb your signal. Capacitators are parts that can "store" electrical energy, and that are able to "release" this energy to supply the load, i.e. your headphones, with the power that is needed to drive them.
2.) The input stage allows you to attenuate the signal that is reaching the "real" input of the amplifier part. That means, you need a potentiometer or a stepped attenuator to control the signal level that is going to be amplified. Or simplified, it is the volume control part of the amp.
3.) The voltage amplifier is doing what it is supposed to do: amplifying the input signal, so that you can get proper volume levels with your headphones. There are a lot of different approaches to do this, and each has it's own characteristics and followers: disrete transistor stages, operational amplifiers (OP-AMPS), tubes.... it all depends on the designer, and the customer
. The different amplification methods often are associated with a certain sound character, e.g. tubes=warmer sound, solid state=cleaner sound...
4.) The output stage is also very important, because the phones which are connected to the amp also need a certain amount of "juice" (current) flowing through them to move the diaphragms, i.e. to produce the sound that the fellow listener wants to hear. The amount of current depends on the "complex resistance" (impedance) of your headphone, the lower the impedance, the more current is "sucked" from the amp, and the better the output buffers have to be.
OK, hope that helps.... it is indeed a VERY simplified look on this kind of stuff, but I hope I got it right (at least a little bit)....
Cheers
Chisum