What is the role of the capacitors in this circuit?
The 10 uF capacitors block DC.


The circuit is a signal or AC amplifier. 
The input is oscillating about 0 V but the amplifier only has a positive supply so it can't swing negative. 
The base resistors bias (add a DC offset to) the transistor so that the output is near half-supply to give maximum output voltage swing. The amplifier output can then swing either side of this voltage in proportion to the input signal.
The input capacitor (to the base) couples the AC signal in and prevents DC going back to the 4 kHz source. As the source voltage oscillates around 0 V the base voltage will oscillate around its DC bias point.
The output capacitor blocks the DC component so that Vout swings above and below 0 V.


This is the configuration of many battery powered or single-rail audio amplifiers.