A power cut was a loss of connection to electricity.
Sometime in the 1970s, there were several consecutive power cuts. People "took advantage of the dark", and many people had sex on these days. As a result, nine months later, there was a "baby boom".
Another such power outage occurred during the Miracle while Gwen Cooper was trying to do research. She and Rhys Williams too "took advantage of the dark". (TV: The Gathering)