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 or Lilith in Tokyo-3. While it is not certain the results of this fusion, it is presumed that the Angels would use Adam or Lilith to unleash an Anti A.T. Field, wiping out the Lilim existence. 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.
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 Lilith 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. When this was completed, the destruction of the Spear of Longinus as well as the Mass Produced Evas would ensure that the process could never be undone and all Lilim souls would be forever united as one being.
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 Sephirotic Tree of Life in the sky, and turns Unit-01 into the Tree of Life. The Mass Produced 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".
This hybrid being 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 the Rei/Adam/Lilith being, along with the Mass Production Eva series, the Spear of Longinus, and Eva Unit-01, proceeds to create an Anti A.T. Field which spreads across the globe, reverting all of humanity to LCL. Lilith begins gathering the now freed souls, which start flowing toward Lilith and her Egg. When this process is completed, Instrumentality begins.
This is clearly not what Gendo had intended, and 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 returns to Earth to live as an individual despite the pain this would inevitably entail. The Rei/Adam/Lilith being falls apart, falls to Earth, and presumably dies. This leaves everyone the choice to leave the ocean of LCL and go back to living as individuals, though only Shinji and Asuka are shown to be still alive. Thus, Third Impact did not ultimately result in Instrumentality because Shinji rejected it.
