Following the Second Impact in 2000 which destroyed half of Earth's population and distorted its environment, NERV referred to Third Impact as an event that would occur should an Angel reach the lowest level of Central Dogma and make contact with Lilith, though they are vague about what Third Impact would actually entail, other than the destruction of the rest of humanity.
In Neon Genesis Evangelion
Near the end of the Neon Genesis Evangelion TV series and in The End of Evangelion film, Third Impact occurs in the form of the Human Instrumentality Project. Rei Ayanami, who holds the essence of Lilith, fuses with the body of Adam in Gendo Ikari's hand, merging her with Lilith and transforming into a gigantic humanoid hybrid. The souls of all humans on Earth are collected by Rei/Lilith and merge into one consciousness, with only Shinji Ikari and Asuka Langley Soryu remaining in their independant bodies and minds.
In Rebuild of Evangelion
In the Rebuild of Evangelion film series continuity, Third Impact instead occurs approximately halfway through the story (at the end of the second film) when Shinji's desire to save Rei causes Evangelion Unit-01 to evolve to a god-like state and begin the event. This is brought to a halt when Evangelion Mark.06, piloted by Kaworu Nagisa, impales Unit-01 with a Lance of Longinus, prematurely ending Third Impact and placing Unit-01 and Shinji into stasis for 14 years.
Despite being interrupted, this Third Impact still manages to destroy most of humanity, though a small segment survives 14 years later.