A dedicated headphone amplifier takes the line output from your audio source and amplifies it to a level that is capable of driving even the most demanding headphones. A DAC takes a digital signal and converts it to an analogue audio signal.
To get the best from listening with headphones a dedicated headphone amp is a very worthy addition to your audio setup. Headphone output circuits often have very little effort given to their design and can provide a very poor quality audio signal. Also many headphone outputs are simply not powerful enough to drive high-end headphones properly. Headphone amps and DACS can be portable, or designed for your desktop.