Star Trek’s red alert -- the sign that the ship is in immediate danger and all crew must report to duty stations -- has been the franchise’s go-to shorthand for impending action since its inception. The accompanying sound of klaxons is as much a part of Star Trek as the sounds of phaser fire or the transporter array, making it a throwaway detail so deeply ingrained in the franchise that viewers hardly ever think of it.
There was, however, an additional alert status known as "Double Red Alert" that appeared briefly in The Original Series. It sounds like a joke, perhaps part of an escalating series that moves to triple red alert, but it did happen in canon and fit Star Trek’s established conditions at the time.
The alert system was the natural offshoot of Starfleet’s presumed military roots and an easily identifiable lexicon on a vessel like the Enterprise. It’s broken down into three general conditions. Condition Green, or cruise mode, meant that everything was normal -- the ship’s personnel worked their normal shifts, off-duty personnel were not required at their stations and all systems were functioning as expected. Yellow Alert was a state of heightened awareness -- weapons and shields remained offline, but the ship’s defensive fields were energized and off-duty personnel needed to anticipate going to their posts if the situation escalated.
Red Alert was the logical end of the cycle -- the crisis is immediate, shields and weapons are charged and the crew prepares for imminent danger. To put it simply, trouble has arrived, and the ship needed to prepare itself. A few other alert conditions appeared onscreen from time to time, most notably Star Trek: Discovery’s Black Alert, which meant the ship’s spore drive was engaged, but in most cases, no one required more than the core three.
That’s what makes double red alert so puzzling. It was only declared once onscreen, in The Original Series, Season 1, Episode 12, “The Conscience of the King," when during the hunt for a murderer on board the Enterprise, Kirk and Spock detect the sound of an overloading phaser in the captain’s quarters. Kirk immediately invokes Double Red Alert, evacuating the nearby crew quarters while he searches the room for the phaser. When he discovers it, he throws it down an emergency disposal chute before it explodes.
The difference between Red Alert and Double Red Alert is never explained, but the incident in “The Conscience of the King” takes place during off-hours, which meant that crew quarters were likely to be full of personnel. In that sense, Double Red Alert seemingly activates all the same conditions as a regular Red Alert, just with a heightened sense of urgency.
Unfortunately, Kirk's line ended up being dramatic overkill. According to Memory Alpha, Double Red Alert was used multiple times in the script for Season 1, Episode 14, “Court Martial,” but the term was changed to a regular red alert and has remained so ever since. The writers probably didn't think much of it at the time, making Double Red Alert another example of a franchise being unaware of how much it was defining itself.