A big capacitor is in parallel with the coil of a relais. from the voltage source the current is limited by a resistor so that the relais will get a delay of about half a second (or more, depending on capacitor) before engaging. while loading the first capacitor a second capacitor is loaded over a timing resistor so that the leds will fade in softly.
As the relais engages voltage is cut off. It takes some time for the first capacitor to empty while the second capacitor is driving the leds for a moment, fading them out softly. After this the cycle repeats. 
Simple as can be...