Third Impact
Third Impact (サードインパクト) is the event, as predicted by the Dead Sea Scrolls in the possession of Seele, which will usher in a new stage of evolution and existence. Third Impact is the culmination of the Human Instrumentality Project.
The event is termed "Third Impact" in reference to "Second Impact", when Adam was awakened by the Katsuragi Expedition funded by Seele. "Second Impact" itself was so termed due to the ruse that it was a meteorite impact.
There are actually several alternate versions of "Third Impact", with different outcomes. Also, some versions can be achieved through several alternate scenarios. Roughly, the potential versions of Third Impact which could occur are:
The Angels' version
Achieved by an Angel reuniting with Adam, being held in Tokyo-3. Unlike the various versions which different humans are trying to achieve, the Angel-version of "Third Impact" does not involve "Instrumentality": trying to forcibly re-unite Adam and Lilith and humanity to achieve a new evolutionary level of existence. The Angels want to reunite with Adam, perhaps as a coherent motive or maybe as simply an instinctive drive, like salmon swimming upstream to where they were spawned. Reuniting with Adam will fully re-activate Adam, which has been reduced to an embryonic state which can be controlled by humans. Reactivating Adam will result in Adam generating a world-wide Anti A.T. Field, eliminating all Lilith-based life on the planet, from bacteria to humans. This would create an appropriate Adam-based eco-system, suitable for the Angels to exist in. This process would leave the Angels as the sole inhabitants of the Earth.
Second Impact was essentially a microcosm of what the Angel's version of Third Impact would be like: all life in Antarctica down to a microscopic level was eliminated, as well as all human scientists in the region; all reduced to the primordial ooze of LCL by having their A.T. Fields nullified by Adam's Anti A.T. Field.
Seele's version
Seele wanted to initiate Third Impact to bring about Instrumentality. They would use an Anti A.T. Field that would neutralize the A.T. Fields that separate human beings from each other, causing all of humanity to revert into a giant ocean of LCL, and freeing their souls. All the souls of Earth would then be collected inside the Adam/Lilith hybrid being and her Egg. This could be achieved through several alternate scenarios involving the Mass Production Evangelions, the Spear of Longinus, Lilith or Evangelion Unit-01 as Lilith's substitute.
Gendo Ikari's version
Gendo Ikari wanted to reunite with his wife Yui Ikari, whose soul was trapped inside of Evangelion Unit-01. It is not entirely clear what the full scope of Gendo's version of events would entail for the rest of the human race (in all probability, all he cared about was Yui). However, judging from Gendo's comment at the beginning of The End of Evangelion to Seele that "destruction creates nothing", it is possible that Gendo's version of Third Impact would not have been as destructive for the human race as a whole compared to Seele's version. As Gendo's full plan was ultimately not realized, it can not be determined with certainly exactly what would have happened. Gendo's version of Third Impact involved the use of (at least) Rei Ayanami (a clone of Yui Ikari which served as a vessel for the soul of Lilith), Lilith, and Adam (which he had fused to his hand). It is assumed that this fusion would allow him to reunite with Yui again inside Eva-01.
Actual Third Impact
Third Impact occurs during the climax of The End of Evangelion. At the beginning of Episode 26', the Mass Produced Evangelions capture Shinji along with Eva-01. Along with the Spear of Longinus, a ritual is performed that creates an inverted Tree of Sephiroth in the sky, and turns Eva-01 into the Tree of Life. The Mass Production Evas unleash their A.T. Fields, causing a giant explosion around the GeoFront. In its wake, Lilith's Black Moon is revealed.
Meanwhile, in Terminal Dogma, Gendo attempts to fuse the Adam embryo in his right hand with Rei. Rei rejects Gendo and merges with Lilith, thus achieving the "forbidden union of Adam and Lilith".
After assimilating Adam, Lilith begins to merge with Eva-01 and the Mass Production Evas. During this process, Shinji's states, "Nobody cares whether I exist or not... Nothing will change. So, everybody just die." This wish seems to manifest itself into reality, as Lilith proceeds to create an Anti A.T. Field which spreads across the globe, reverting all Lilith-based lifeforms into LCL. The liberated souls of humanity are gathered by Lilith and funneled into the Black Moon (her "Egg"). When this process is completed, Instrumentality begins.
This is clearly not what Gendo had intended, but the Seele council seemed fairly content with the outcome (even if it had not happened quite as they had planned). However, Shinji Ikari ultimately rejects Instrumentality, and the Black Moon is destroyed, dissipating the souls back across the Earth and into the oceans. Lilith's body falls apart and descends to Earth, and she apparently dies.
All disembodied individuals are left with the option of recreating their bodies and returning to a life in the physical world, regardless of the pain it would inevitably entail. Shinji, and later Asuka, return to the vicinity of Hakone, but the fate of everyone else is left open.
