Sunset Over Venus refers to this event as the 2049 Moon Crisis.
Talk about it here.
The moon crisis was the incident in 2049 in which the Moon was revealed to be an egg, which hatched before laying another egg to replace the moon as it set off for space. (PROSE: Sunset Over Venus, TV: Kill the Moon)
History
Prelude
In 2039 the crew of Minera Luna San Pedro, a Mexican moonbase, founded to search for minerals, disappeared. (TV: Kill the Moon)
Crisis
By the year 2049, giant vicious red and black spider-like creatures with sharp teeth inhabited the Moon, living in the caves on the surface and killing every astronaut visiting the Moon, and covering moonbases in web. The Twelfth Doctor, Clara Oswald, Courtney Woods and Lundvik discovered these creatures on a mission to find out why the gravity had increased, with Courtney managing to kill one. They were connected to the organism that had been growing for millions of years inside the Moon, which hatched soon after. It laid another egg, which replaced the original Moon. The original moon then flew off to roam all of space. (TV: Kill the Moon)
Legacy
The Twelfth Doctor credited the day that the creature hatched and had its life spared as the turning point where humankind began "creeping off" into the stars. (TV: Kill the Moon)
To the general populace of Earth, the moon crisis would be, in the words of 2119 native Alice O'Donnell, remembered as the time when "the Moon [exploded] and a big bat [came] out". (TV: Before the Flood)