Significance of Capacitor Attached to output
Since your earphone is a dynamic speaker, it's only sensitive to AC.

Thus, a high value C2 is in place to block DC from flowing through the speaker. It doesn't stop AC.

That way, the designer of the amplifier circuit doesn't have to make sure the "zero" output voltage (ie. output with perfect GND-level input) is really bias-free (ie. at perfect GND-level itself).  That's a good thing, because Opamps aren't perfect and typically do have some DC offset. 

And that offset would  lead to a constant bias current through the earpiece, which reduces sensitivity of the same, and increases power consumption, without any benefit.