Why place capacitors in front of the line to a (headphone) audio speaker?

The two large capacitors are acting as AC coupling capacitors. A capacitor in series with a signal acts as a high pass filter (if you're curious about that, look into the impedance model of capacitors).

Basically, the smaller the value of the capacitor, the higher the cutoff frequency and so more of the low frequency signal (in this case, the audio bass) is going to be filtered out.

The reason why the capacitors are so large is so that the cutoff frequency is lower, filtering out the DC bias while also keeping more of the low frequency signal. The DC bias would just drop across the speakers and dissipate extra power.