How do amplifiers work?

My belief is that the amplifier takes electricity from the wall and stores it in capacitors (like big batteries).
The music signal (from a CD player, etc.) is used to modulate a "valve" (a tube or transistor) which results in a mirror image of the input only stonger.
Think of turning a water faucet on just a little then cranking it wide open then turning it back down, etc. This is modulation (only you are using the stored electricity not water).
This "stronger" signal is sent through your speaker cables and is heard (through your speakers) as music.

Here's how I look at it: electricity is generated by converting one form of stored energy into another. Moving water, wind, or steam made from fuel spin turbines which are like big reverse electric motors. In your home there are wall outlets. The power company regulates the energy available from them at a set standard. Using standards makes it possible to reliably run devices connected to the system.

Until you connect something that uses electricity (a load) to the outlet, nothing happens, no energy flows. Audio gear operates with its own set of standards. This allows different brands to work together. By itself, the amplifier is both a energy converter and a storage device. The amplifier has a missing part which is completed when you connect your speakers. The speakers motor electrical energy into moving air. How much air? That all depends on what qualities you want your music to have.

A CD player converts a set of digital instructions into a regulated energy flow. Likewise, a phonograph converts a set of molded plastic instructions into an energy flow. The preamplifier converts the flow into a form that the power amplifier can use. The power amplifier converts the flow into a form the speakers can use.

How well all these conversions take place is a matter of choice. The choices designers make result in performance limits. The limits of performance are conveyed to you as specifications. For example, when the conversion is out of whack (distortion) by 1% over a certain range of instructions an amplifier is said to have the capability to steadily produce so much power. Increase the distortion you're willing to accept and the amplifier can have a higher power rating. Limit the range of instructions sent to it and again the rating looks better. Don't be fooled. The important thing to remember about the power rating is that it is a description of the amp's capability, not a description of its moment to moment operating condition. An amp rated for 100 watts continuous may indeed momentarily output one or 300 watts.

An amp's capability derives from how well it converts, stores and regulates energy, how it controls heat, how well it converts its instructions, and the length of time it can be expected to do these things before it fails. Bigger is not always better. If you want to amplify music so 50,000 people in a stadium can hear it or if you want to blast your stereo at home you'll need different amplifiers to suit each application. Regardless of its specs, how subjectively well the amp fits your application is a matter of perception.

Nice posts, guys. Even simpler, think of an amp as a signal-modulated power supply for your speakers, properly hinting the importance of its power supply design and execution.

Thanks for the great responses!
One thing that still confuses me is the wattage output during peaks in the music. I'm not sure the best way to phrase this, but for instance, during a heavy bass note, combined with any number of other instruments, when a large amount of power is being drawn, does the amp typically send more wattage than it is rated for(continuous rating)? I read one thread where an owner of a Plinius amp rated at 125watts, said that the amp could output, at peak moments, up to 1000watts before clipping. Where as another Plinius amp, which was rated 150w or 200w, clipped at a much lower level. Obviously the 125w amp is of better design, but how does all this work(stored power?, dynamic headroom?), and what is the typical output of most amps, aside from continuous power. Can small (under 100watt) amps, actually output clean, but brief bursts of wattage that far exceed 100watts? and by how much? and how does one know this? I've never see it in the specs I've read, or don't know what to look for.

Yes, an amp does have peak power normally quite a bit in excess of its nominal continuous rating. The class in which the amp works, the size of its power supply and whether it is stiffly regulated or not are all factors in by how much an amp will exceed its average rated power on peaks. Interestingly enough, in the days when objective measurements were not met with some kind of exorcism rite there was a spec often provided as to the “dynamic headroom” of the amp given in dBs. High Fidelity magazine also touted rating power amps in dB watts so that the single number given would correlate better with the ability of the amp to actually produce an increase in SPLs. The single most significant number that would address your concerns though is the dynamic headroom figure. Dynamic headroom probably accounts in great measure for this subjective audio notion that, based on listening to different power amps (ostensibly in the same system and the same room, but subjective audiophiles are not prone to quibbling over mere details such as limiting the number of variables), you get your "bigger watts" and you get your "smaller watts", then you can also get your "tube watts" and your “solid state watts". All this constitutes, in all likelihood, more bogus observations from the subjective front. It can all be explained "scientifically" and far better than by a duffer like me. Good day.