In 2000, a group of scientists conducted an expedition in Antarctica where a large being of light, deemed by them as the first Angel,Adam, was discovered. On September 13an attempt was made to capture it which ended in apparent failure when it proceeded to self-destruct, creating what would be called the Second Impact. The true nature of the Second Impact was concealed from the general public, who was led to believe that the devastation was caused by a small meteorite traveling close to the speed of light, impacting in Antarctica.
In the conflict with Angels, mankind is represented by the mysterious organizations NERV,GEHIRN(which started out as the investigation team for the Second Impact but became NERV later on), Seele, and the Marduk Institute. NERV is, in theory, under the control of SEELE, but NERV has its own agenda, driven by its commander Gendou Ikari. NERV carries out two tasks: to defend the Earth from Angel attack with a small number of Evangelions (Evas), and the Instrumetality Project, which, according to Gendou, is the path to becoming one with God.
The Evas have the outward appearance of massive humanoid robots and can apparently be piloted only by children conceived after the Second Impact. Pilots are selected by the Marduk Institute, which is later discovered to be composed of about 108 ghost companies, but Gendou Ikari and Ritsuko Akagi are actually in charge of selecting pilots. It is frequently speculated that qualifying pilots must have lost a mother, whose soul is used as the soul of the Eva. (This has been debated due to the probability that Rei is a clone of Yui and therefore doesn't have a technical 'mother' but some fans believe that Yui's soul was split between Unit 00 and Unit 01. This theory coincides with Rei and Shinji's ability to synchronize with each other's Evas.) The Evas also appear to behave under the influence of the soul inside it. One example is when Unit 01 goes "berserk," acts without control of its pilot or NERV and refuses to shut down (or in one instance, to start without Shinji). Unit 00 goes berserk and lashes out at the tormentors of Ritsuko Akagi's mother, apparently attempting to kill Rei. Though unit 02 does not ever go truly berserk, Asuka says in "The End of Evangelion" that she feels the presence of her mother protecting her in the Eva. The term "berserk" really only befits the actions of Unit 00; Unit 01's actions were focused, restrained, and beneficial to Nerv's missions.
Each Eva has its own designated pilot, due to the bond between the pilot's soul and the soul of the Eva; otherwise, any other person who tries to synchronize (simply put, to technically work as one mind) with the Eva is more likely to be refused. That is not to say that it is impossible to synchronize in such a situation, as is shown in an experiment in Episode 14, in which Rei and Shinji synchronize with each others' Evas. It is later apparent that the Evas are not really "robots" but rather living, biomechanical organisms, in contrary to the popular belief of the general public. While Ritsuko does mention at the beginning of the series that the Evas do have some biological components to them, the extent to which the Evas are biological is not immediately apparent; it is finally revealed, towards the end of the series, that Evas are essentially Angels (made from Adam, the first Angel, except unit 01 which is almost certainly made from Lilith, the second Angel) onto which mechanical components are incorporated during its creation — part of the reason being to restrain and control them.
The secret second task, the Human Instrumentality Project, intends to start an artificial evolution of mankind. Considering the religious implications of the term evangelion this event was said to bring about the salvation of mankind in the context of a newly created Earth and humanity's becoming one with God. SEELE is the main driving force behind this project, for reasons unknown, but they mention that humanity must evolve or it will die, thus the need for a forced evolution. This artificial evolution strives to merge all human souls into one by disposing the individuals of their AT Fields that separate egos from each other. This causes their bodies to revert to .LCL When everyone comes to this state, they will no longer feel the pain or loneliness that would typically precipitate from interaction between humans; it is comparable, but not equal, to death.