Without the capacitor, a DC coupled input will pull the base down to ground, biassing the transistor off.
In this case, the capacitor is being used as a coupling capacitor, that transmits AC signals, while allowing a DC voltage to exist across it without a DC current flowing.
Capacitors are used here in order to pass the audio signals without its DC level is interfering with the transistor's bias.
For instance, one transistor has a collector voltage of 5V, and you are directly connecting the 1v base biased transistor with it will always turn on the second transistor which means the DC level of the first transistor will interfere with the audio signal that is passing to the second transistor.
If you use a capacitor in between these two transistor, it will only pass the audio signals to the second transistor and it prevents the DC interference.