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If you have been set this as a homework question, your teacher really does not like you. This is my take on the circuit.
Firstly D1 - D4 is a bridge rectifier, so any ac voltage coming in to RCX develops a dc voltage across C1. This is used to power the op amp. I can only assume that this is the intention of the circuit - that the op amp is meant to be powered from an incoming signal.
R2 and D7 provide a contant voltage (5.1V) at the top of CdS1, regardless of the incoming signal. This is then fed to CdS1 and CdS2 which form a potential divider (reduce the 5.1V down to a lower voltage, depending on the ratio of CdS1 and CdS2). This is buffered by the op amp - the op amp is doing nothing more than adding a bit of 'drive' to the voltage at the junction of CdS1 and CdS2.
Now here comes the tricky bit. It looks like the voltage at the output of the op amp changes the load seen by RCX. Assuming the output of the op amp is a fixed dc voltage, this clamps the cathodes of D5 and D6 to this voltage. This in turn clamps the voltage at the anode of D5 and D6 which has the effect of clamping the input signal.... which is being used to power the op amp... so unless you get your circuit components correct, I can see this circuit running into startup problems.
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