Transparent as in it does not add anything to the signal.
In the case of an amp, a transparent one only amplifies it, so that more demanding headphones will receive enough power to give you enough volume.
In case of easy to drive headphones (ie the ones made for computer / portable / gaming use), adding an amp is not needed.
However not all amps are transparent. In fact most of them are "colored" and therefore you can hear "improvements" when using them.
There is also the case that things "sounds better" just because you are listening to them at a different (usually higher) volume.
Edited by Calbert - 3/13/14 at 9:11pm