What do Capacitors do in a System with a Speaker?
The capacitor in series with the speaker is to block DC.

The 555 output can only swing between the 6 V power and ground, so has a net DC bias of 3 V on average.  This DC does nothing to make sound come out of the speaker, but limits how much the speaker can deflect in one direction and would draw significant current from the 555 timer if the speaker was connected directly.  The DC resistance of a speaker is quite low.  The capacitor allows only the AC component of the 555 output voltage to cause any current thru the speaker.  You can only hear the AC component from a few 10s of Hz upwards anyway.