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Depends on the amp design. To have amplification, you need some kind of "active" component: transistors or tubes are the simplest. You also have complex components like op-amps which are many transistors and other components put together onto a single chip.
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They amplify.
A single transistor is an amplifier, but it has many non-ideal characteristics. You can't just run music through a transistor and get something good-sounding on the other end. (But you
would get louder sound out of it! This is one of the first tests the inventors of the transistor did: hook it up to a speaker and make it amplify the music. It works, it just isn't particularly pleasant sounding.)
A practical transistor audio amplifier has multiple transistors along with many associated components (resistors, capacitors, etc.) hooked together in an arrangement that attempts to minimize distortion.
An op-amp is, in many ways, an amplifier on a chip. You still need to add outside components to make it useful as an audio amplifier, though.
Tubes are similar to transistors: each one is an amplifier, but you usually end up using several to make a useful audio amplifier.
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| What are the factors that make one headphone amp, whether stand-alone or built into a portable device or home component, sound better than others? |
It all comes down to distortion. Some distortions are unquestionably bad, and amp designers seek to minimize them by adding components. Other distortions add "flavor" to the amp, but not everyone agrees on the best ways to combine these; it's kind of like cooking.
Reducing distortions sometimes involves removing components, but more often it involves adding them or using better types. This is the reason better amplifiers usually cost more: they have more stuff inside.
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| Why do some devices/amps and headphones seem to work well together? |
Part of it is the "flavor" issue. Headphones are much less balanced than even humble amps, and sometimes they require counterbalancing flavors in the amp. For instance, some people find Sennheiser headphones laid-back and boring, so pairing them with a snappy-sounding amplifier brings the system into balance for them. Pairing that same amp with "forward" sounding headphones might be too aggressive, though, so you'd maybe choose a more neutral or laid-back amp to compensate.
The other part is that different headphones cause the amp to distort in different ways because they present differing loads to the amp. One of the things that distinguishes a really good amp is that it drives most all headphones well, because its sonic character doesn't change as you try different headphones; the changes you hear should be due to the headphones alone, in a high-end system. You pick the headphones based on their sonic signature and know that your high-end amp will drive them competently, letting their true character through, whether for good or ill.
