well sashava you are almost right, line level refers to a 2v (single ended), or 3vrms+ (balanced) line level analogue signal. it does not necessarily pass through an amplifier at all, some dacs will have an internal current to voltage stage and directly output line level signal, some will output current which needs to go through an IV stage to produce the line level signal. it is these conversion stages, some of which might be as simple as a single resistor or a line transformer, the quality of the dac chip itself, the handling of the digital input signal and the choice of layout, circuit design, power supply and components in the output stage that produce different quality and sound signature of the resulting line level output.
by the way, line level output is usually enough voltage to drive most headphones without amplification, its the current that needs to be amplified in most cases. this depends on the headphones, higher impedance headphones will need some voltage amplification as well.
