Based on the real-life Giant Impact Theory first proposed in 1975 by Dr. William K. Hartmann and Dr. Donald R. Davis.
The theory states that shortly following the formation of the Earth (approximately 4.5 billion years ago), a rogue Mars-sized planetoid called Theia (also sometimes referred to as Orpheus) impacted the Earth, ejecting a significant portion of the Earth's mantle into space. A ring of debris formed around the young planet, which eventually coalesced into the Earth's Moon.
Samples of moon rock taken during the Apollo Moon landings show an oxygen isotope composition that is nearly identical to the Earth's mantle, supporting the theory. The impact is believed to have either destroyed Theia, or buried it deep into the Earth, possibly merging it with the Earth's core.
The First Impact is mentioned, but not depicted in the Neon Genesis Evangelion. In the series, the event is believed to have been caused by the accidental arrival of a second seed of life, however it is unclear if that was the Black Moon or the White Moon. This in turn results in conflict between two distinct forms of lifehumanity and the Angels.
The name Theia was derived from ancient Greek Mythology. Theia was a goddess, one of the Titans that preceded the more well known Olympian Gods. Her husband and brother was Hyperion, with whom she had three children; Helios (the sun), Eos (the dawn), and Selene (the moon).