|>>|| No. 26057
Stereo receivers usually have a perfectly satisfactory headphone amp, as do most audio interfaces and mixers.
The problem is generally with battery-powered equipment. To save on cost, weight and power consumption, they tend to use a fairly weedy headphone amp IC that is designed for sensitive, low-impedance earbuds. Some of these amplifier chips deliver as little as 25mW peak, but a very large pair of headphones could need as much as 400mW to perform properly at high volume.
The most common symptom of an inadequate headphone amp is poor bass response. Poor transient response is also fairly common and occasionally you'll hear distortion during high-energy sections of audio.
If you're plugging AKG K701s or Beyerdynamic DT990s into a phone, you'll probably want a little FiiO amp to get the best out of them. Otherwise, the benefits of a dedicated headphone amp will be fairly minor.
DACs are an altogether more complicated topic, but diminishing returns kick in fairly quickly here. Some cheap consumer hardware is equipped with a genuinely bad DAC, but you don't have to spend a fortune to get something very good. The difference between a £150 audio interface and a £2000 converter from the likes of Prism or Benchmark is so subtle that 99% of people won't hear any difference.