Confusing dark sensor circuit diagram
This is a crappy circuit.  Run away.

It seems the intent is that when there is lots of light, LDR1 goes down in resistance, which turns on Q1, which turns off Q2.  When it's dark, Q1 doesn't turn on enough to pull down the base of Q2, which then is able to turn on the LED.

However, there are some problems here:

The circuit is highly dependent on the gain of Q1.  Transistor gain can vary widely across parts, even from the same batch.  If you happen to get one with high gain, Q1 might never be off enough to allow Q2 to come on.

There is nothing limiting the current thru the LED.  There should be a resistor in series with the collector of Q2.

It would be useful to have some hysteresis.  This circuit will fade on and off at the threshold light level.



See https://electronics.stackexchange.com/a/53681/4512 for a circuit that actually does what you want.