The alternate reality created in 2233 when the Romulan mining ship Narada emerged from the future and destroyed the USS Kelvin, setting the lives of Kirk and his crew on a different course.
The Kelvin timeline is the setting of the films Star Trek (2009), Star Trek Into Darkness and Star Trek Beyond. It splits from the original history when Nero's ship Narada, thrown back from 2387, attacks the USS Kelvin and George Kirk dies saving his crew as his son is born.
From that point events diverge. James Kirk grows up without his father, Starfleet's ships and technology develop differently, and in 2258 Nero destroys Vulcan, killing Spock's mother Amanda. The elderly Spock of the original history, also stranded there, helps the survivors found a new colony.
The name comes from the lost starship and was adopted to distinguish this reality from the prime timeline. Discovery later refers to it in passing through the story of a time-displaced officer.