The output of the 555 goes high and turns on the transistor which turns on the relay. Then the output of the 555 goes low which turns off the transistor and relay. When the transistor and relay are turned off then power is not used for the repeller.
The datasheet for the 555 shows how to calculate the output high time and the output low time. Then you can calculate the percentage of time when the repeller is turned off and calculate the amount of power saved.
Google says that an ultrasonic mosquito repeller DOES NOT WORK! It might attract mosquitoes. But an ultrasonic squirrel repeller might work.