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.
Portable electronics devices, such as the iPod, MP3 players and laptops, often benefit from the addition of a dedicated headphone amplifier and/or DAC.