Headphones are really just small speakers.
The amplifier that drives them is of paramount importance to how they sound. Many CD players and pre-amps have headphone outputs on them. When using audiophile-type headphones with higher impedance, it takes a fairly high voltage level to get a reasonable volume. The cheap headphone amplifiers in CD players and preamps simply cannot generate the required voltage swing without clipping off the musical peaks. A good tube amplifier has much more peak voltage capability than almost any solid-state amplifier.