First, you have to verify that the transmitter send out signal at which frequency (you can check this by calculating central frequency of LM567, refer to LM567 datasheet).
Because, received signal is week so that, after detect the signal, we have to amplify it, then the LM567 do this task, if the main frequency of the signal is the same as the central frequency of LM567, then the output pin is grounded (or high, I don't remeber), this causes the relay be on or off.
The above is the main idea of your circuit. You can simulate it using Circuit Maker or some similar softwares.
Any question?