The knock sensor signal passes through C1, which blocks any DC current between the ECU knock sensor circuit and this amplifier circuit.
R1 is the volume control. When the wiper is all the way down (at pin 3), then the inverting and non-inverting inputs of the amplifier are getting the same signal, so there should be no output. When the wiper is all the way up (at pin 2), the inverting input is getting very little input, and the amplification will be at its maximum.
C2 blocks DC to the speaker (or headphones). R2 is a limiting resistor, to be used with headphones only, to prevent power up spikes from possibly damaging the headphones. This will also significantly reduce the power output of the amplifier. This seems to work well with walkman type headphones, but for a speaker (or any case where you cannot get sufficient volume), this resistor should be omitted.
R3, C3, and C4 form a noise filter for the power supply. The reason for using a small capacitor like C4, is to kill high frequency noise. A relatively large capacitor such as C3, often has too much internal inductance to be effective at high frequencies.