How does this LDR controlled light work?
For reference and to protect against future edits, here is the circuit being described:



When analyzing such things, it can be helpful to consider the limiting cases.  In this example, they are the LDR (R1) being a short and being infinite.  Let's examine each case.

When R1 is a short, then the B-E voltage of the transistor is 0.  That keeps the transistor off.  That means no collector current will flow, so the LED (D1) won't light.

When R1 is open, current can flow into the base of T1 thru R2.  Figure about 700 mV for the B-E drop of T1, which leaves 5.3 V across R2.  By Ohms law, the current thru R2 is therefore 530 &micro;A.  That is also the base current, since that is the only place the current thru R2 can flow.

If T1 is saturated (we'll check this shortly), then figure the collector is at about 200 mV.  If this is a typical green LED, it drops about 2.1 V when normally lit.  That leaves 3.7 V across R3.  That results in 14 mA thru R3, which is also thru D1.  14 mA should quite nicely light any ordinary indicator LED.

That was assuming T1 is saturated.  Let's see what gain it would need for that to be true.  We already know the collector current would be 14 mA, and that the base current is 530 &micro;A.  That comes out to a minimum gain requirement of 26.  Just about any small signal transistor can do that at these current levels, so T1 is in fact saturated.

So to review, D1 is off when R1 is shorted, and nicely lit when R1 is infinite.  Somewhere in between there is a transition region between full on and full off.

This circuit "works" if the LDR was chosen so that its resistance is somewhat below the transition point when light, and somewhat above when dark.  Since you haven't given any particulars about the LDR, we can't say if it's light and dark resistances are suitable for this circuit.  However, the basic idea is workable for a crude "night light".

A better circuit adds some positive feedback, or hysteresis.  That causes the circuit to snap between the on and off states.  For more information, see my answer to a similar question at https://electronics.stackexchange.com/a/53681/4512.