The input and output blocking capacitors acts as short circuit for AC signals and prevents DC signal transmission from DC power supply to AC signal source and to output by blocking DC signals.
Emitter bypass capacitor acts as short circuit for entire bandwidth of AC signal to be amplified thereby shorting the emitter degeneration resistance (which reduces gain) so that the amplifier gain will be large. For the signals frequencies out of interest i.e. frequencies lying outside frequency spectrum of input AC signal to be amplified, bypass capacitor acts as open circuit so that the gain of amplifier gets reduced due to emitter degeneration resistance thereby improving the efficiency of amplifier. The DC biasing currents and voltages are unaffected by bypass and blocking capacitors as they act as open circuits for DC signals (Impedance offered by capacitor is Xc = 1 / (w*C) where w is frequency of AC signal, w=0 for DC signal, C is capacitance).
FOR DC - capacitor OPEN
For AC - Capacitor CLOSE