Digital to Audio Converter: a sound card basically.
For most of us we say DAC because most of our "sound cards" are not inside our computers, and some don't even use USB. As long as the devices converts digital information into sound, it is a DAC.
Sound cards however, are not just DACs since they have their own built in amp to power whatever you plug in. A dedicated DAC such as the ODAC or the ELE D01 would not provide enough power for the headphones to reach their potential. This is where an amp comes in.
The reason why we tend to lean towards external DACs, than ones inside computers are design orientated: the power regulators in a PC is clean for the electronics being put inside, but is not clean enough to create a noiseless background for any speakers attached to it. Whereas an external DAC, whether it is USB or Optical, can have dedicated power regulators to clean up the "buzzing" sound. The next section of this hobby also revolves around amps and how their design impacts the sound. But that's another thread in itself.
But as far as I can tell. The ADX700 shouldn't be too picky whether it's plugged into a sound card, directly into a DAC, or a desktop sound system. Just avoid onboard sound like the plague.