At the end of the century, a gigantic meteorite crashed into Antartica. This event causes half of the population of earth to perish due to the melting of the polar ice caps, wars and the appearance of the mysterious beings known as Angels.
But that was just what everyone was told.
The truth is another matter....
The truth is that mankind was poking it's nose where it shouldn't have been. The dead sea scrolls, which had been interpreted, foretold that man could attain a higher level of being. The catch was, that mankind would have to defeat 17 beings of immense power. In Antarctica the first of these beings was discovered, which unleashed a horrorfying eruption of power now known as the "second impact". These beings became known as "Angels".
A third impact would likely destroy the human race entirely. With little hope of standing against the power of the Angels, the United Nations decides to fund a new organization which would study and hopefully lead to the prevention of a possible third impact. This organization, headed by Gendo Ikari, is known as NERV. The truth is, that NERV is serving the compilation project which will facilitate man's evolution into a higher state of being once the Angels are defeated. This is what the Angels are set to prevent. NERV develops the Evangelion as a counter to the Angels, and is the only weapon in existance which can stand against them. Should the Evangelions fail, man will become extinct.
So how did NERV come to select it's pilots? Well obviously, the person has to be capable of synchronizing with the Eva. But what type of person would that be? Someone that spends years training to synchronize with the Eva? No, fourteen year old kids of course! This is anime after all. Training means nothing compared to the powers of young teenage Japanese school girls. Later on, Shinji was found to be capable of piloting an Eva (even though he's a boy).