In the English dubbings of Evangelion, Destrudo (also referred to as Destrado) is mentioned only once in The End of Evangelion, just prior to the Third Impact. The term is used several times in the Japanese release of the series, often as a form of techno jargon.
As described by the Freudian Psychology Theory, Destrudo is an innate emotional impulse to destroy both oneself and everyone around them. It opposes the Libido, which is the urge to create. The manifestation of one's Destrudo is a major concern for the Evangelion pilots, as the constructs they control are so deeply entwined with their own psyche.
In The End of Evangelion, while the Destrudo reference is cryptic and unelaborated, it actually goes far to explain the driving force behind the Third Impact, as well as Shinji Ikari's desire for everyone, including himself; to die. It is in fact Shinji's Destrudo that is manifested at the Third Impact, and is the trigger for Lilith's cataclysmic Anti-AT Field.