Double red alert was a alert status signal for extremely dire situations, especially when a nearly instantaneous response was required. The alarms and lights for a double-red alert were the same as for a standard red alert.
In 2265, Captain James T. Kirk called for double red alert when Spock detected the distinctive sound of a phaser on overload hidden in Kirk's quarters. Realizing that there were only a few seconds available to evacuate that section of the ship, Kirk ordered a double red alert. (TOS episode: "The Conscience of the King")