Line Out Dock - a cable that connects to the player's dock connector that draws out the line-out signal. Usually has an 3.5mm mini plug on the other end so user can plug into an portable amp.

Here is how things work in DAP:

Music data -> CPU -> DAC -> AMP -> headphone.

DAC - Digital-to-Analog Converter, turns digital data to analog sound.

AMP - Amplifier, amplify the signal (music) from DAC to different set of gain (kind of like volume control).

In portable device, due to size restriction, the amp section is usually kept very simple and just enough to drive normal, easy to drive headphone. Some time, cheap SMD components (tiny resistor, capacitor, lousy chips) are used to cut cost and space - these result in a headphone signal that are sub-par. In order to extract as much sound quality as possible from the portable device, we use the line-out signal. Line-out means the signal is directly from the DAC, un-amplified (so it avoids all the sub-par components in the amp section). We connect the line-out to an external amp (which replace the function of the internal amp section), which hopefully will be a lot better than the internal amp and thus provide better SQ and more power to drive difficult-to-drive headphones.

Of course, the assumption is the internal amp is not going to be as good as (or as powerful as) the external amp you are going to use, or else the improvement will be really minimum (or none).