One aspect of it is that not all power is created equally. Say you have an amplifier that can do 2W peak output. The following graph for this theoretical amp shows Power (as a function of V and A) aswell as Voltage (limited to 10V) and Current (limited to 0.5A).
The X-axis is resistance from 1 to 1000 Ohm.
Depending on what resistance your headphone presents to the amp, it will find itself somewhere on the yellow curve.