This movie is horrible and I have lost all respect for the creator. Every single character was ruined by doing things they never would have done if they were consistent with their personalities in the original series. The fan service was in horrible taste and I couldn't tell if I was watching soft porn or a sci fi movie. It was also one sided, with fan service targeted only at males and nothing for women. The only reason I suffered through this 0-star piece of horseshit was to try to understand the plot. Here are the conclusions I reached.
*****SPOILERS***********
LILITH. In addition to serving as the model for Eva creation, Lilith is the mother of humankind (though we don't know when, why, or how she created the first people). The humans, which collectively make up the 18th Angel, have both Adam and Lilith. The Angels are born of Adam and wish to return to Adam, who also came from Lilith. I guess Lilith is basically "God". 
SECOND IMPACT. The Second Impact was the fusing of Adam and Lilith, which caused an explosion powerful enough to melt Antarctica. Losses were minimized since the event was engineered by humans. Presumably, the Second Impact was a test run for the Third Impact and subsequent Human Instrumentality. (If Adam and Lilith did not fuse, SEELE planned to cause the Third Impact by putting the new Eva series in contact with Adam.)
INSTRUMENTALITY. SHINJI'S CHOICE. The Third Impact differs from the Second because this time the 01 Eva had awakened. When this being joined with Lilith, it gained the power to decide whether people would all keep their human forms or exist forever in the world where their souls were one. Shinji chose for people to take back their forms. However, it is unclear whether he restored all humans or only himself and Asuka. 
...And as for the ending... I got nothin'. Maybe Shinji snapped and turned into a violent psychopath after living through so much trauma? Who cares though, the movie is a godawful shitfest either way.