"The Vulcan Hello" was a term used by Commander Michael Burnham to describe how the Vulcans dealt with their encounters with Klingons in the aftermath of a fatal clash near H'atoria in 2016, which led to the destruction of a Vulcan ship.
Following that fateful event, and because "Vulcans never made the same mistake twice," any future contact made with the Klingons was answered with immediate weapon's fire as a sign of strength and respect.
This information was given to Cmdr. Burnham from her mentor, Ambassador Sarek, during the USS Shenzhou's mysterious confrontation with a Klingon vessel in 2256. After learning of this Vulcan practice, Burnham strongly recommended that they fire at his ship, however her recommendation was dismissed by Captain Philippa Georgiou, who responded that the Federation never fires first. (DIS: "The Vulcan Hello")