A: What you plug your headphones into can significantly affect their sound, and the quality of the amplifiers built into portable CD/MP3 players is generally awful. It's not their fault: the little guys have to power their electronics and their internal amplifier using a few puny volts. Even some of the better home AV receivers' headphone jacks offer highly variable sound quality.
Marketed claims such as 'frequency response 4 Hz to 20 kHz' are usually overstatements; the product's response at frequencies lower than 20 Hz is typically very small. Headphones are also useful for video games that use 3D positional audio processing algorithms, as they allow players to better judge the position of an off-screen sound source (such as the footsteps of an opponent or their gunfire).
Every single Bluetooth codec has significant quality issues—despite many creative solutions employed to make the most of the limited bandwidth the standards employ. For those keeping score at home: not a single codec available can meet wired signal quality. Though Bluetooth audio has come a long way since its noisy beginnings, it’s still not ready to replace the headphone jack. Qualcomm’s aptx HD, and Sony’s LDAC 990kbps codecs come close, but everything else falls far short of the mark.
Although some headphones available are wired, many more are available that are wireless, and use Bluetooth to enable your music to be heard, even if the stereo or other device is several feet or even a few rooms away. Wired headphones deliver superior sound quality to wireless and Bluetooth because there's no chance of picking up interference from other devices, which sometimes happens with wireless headphones. In addition, wired headphones have no batteries to power them, so there's no chance of interruption should the batteries wear out.