Hi,
Where is the "delay" in the circuit?
There are various circuit configuration of an LDR, one of which is the one you posted. From a typical LDR function, the LDR is use where it is necessary to detect the presence or the level of light. Values of the resistance of the LDR may change over many orders of magnitude the value of the resistance falling as the level of light increases.
In the circuit, the relay functions as a switch. When it hasn't reach the threshold of the diode, it will not conduct. Meaning, current won't flow in that direction.