Having trouble with light activated circuit.
Understanding how the circuit works requires that you know how a photocell responds to light. 

I'm assuming that you are using a standard CdS photocell. These have high resistance in the dark and the resistance drops to a low value in the presence of light. 

When the photocell is dark, timing capacitor C1 is held High by R1.  When the photocell is exposed to light, the voltage across the photocell drops to a low value. D1 prevents C1 from being discharged by the photocell. 

Instead, C1 slowly discharges via the 1M resistor. When the voltage across C1 drops to about 1/3 the supply voltage, the output of the 555 timer goes Hi and turns on the tone generator.