Question about bjt audio amplifier circuit
C1 protects the dc voltage at the base being altered by a signal source that has less-than-infinite dc resistance. It is vital that the bias conditions on the base is not compromised by the signal source impedance. C1 allows ac signals to superimpose on the bias voltage at the base.

A voltage divider bias sets a fairly guaranteed voltage at the base. The alternatives are trying to feed a precise current and relying on hFE OR using dc negative feedback to set the collector quiescent voltage at a mid point between the power rails.

Relying on hFE is going to end in failure because a stable value of hFE relies so much on temperature being kept constant and the transistor not ageing its hFE. 

Using a feedback resistor is sometimes used especially when the emitter resistor is zero ohms because circuit gain can also be controlled BUT it is only really useful when input and output signals are not expected to be a large percentage of the power rail i.e. don't use it if you want a large peak to peak output voltage.