On October 2nd, 1988, an artifact from out of nowhere landed in what Sparrow calls the "Primary Universe"--life as we know it. The origin of this artifact, the jet engine, is a "Tangent Universe", created when the jet engine blew through the wormhole and into a day that had already happened, October 2nd.
The artifact marks the arrival of the Tangent Universe. If you've been observant you'd realize that this introduces paradox--the Tangent Universe from which the jet engine came did not exist until the jet engine exited its domain via the wormhole, hmm.
These paradoxes are inevitable when dealing with time travel. They don't fully discount the possibility of time travel, they just mystify it beyond any sort of simple comprehension. I find that it's easier to visualize the two universes if you imagine the Tangent Universe actually "happening first".
After 28 days of a turbulent existence, the Tangent is erased when the story jumps back to October 2nd in the stable Primary Universe (of course, this is just a model for visualization, these universes existed concurrently).
The instability of the the Tangent Universe meant it would collapse within weeks, destroying all existence with it (as Sparrow explains). Ultimately, Donnie Darko closed the wormhole by ensuring the artifact's passage through it, back to the Primary Universe (which would seem to be the "second" time it happened, but again, time travel presents paradoxes).
In doing so, the jet engine was sent back hurdling toward the Darkos' house, except this time Donnie knew it was coming. Donnie just smiled, because he knew that he had restored the world to its proper state, and in doing so, saved Gretchen, his mother, and his sister (an airplaine missing an engine doesn't stay in the air too long). Donnie was only able to find the courage to accept death because he knew he wasn't dying alone. By his brief but profound relationship with Gretchen, Donnie overcomes his fear of dying alone. Recall the dichotomy of fear/love theme
(complemented by the Primary/Tangent dichotomy) that was r einforced by the role of self-help guru, Jim Cunningham, throughout the film. Donnie fights this battle and ultimately overcomes his fear by finding love in Gretchen. In the end, Donnie not only saved those closed to him, but the world and all of existence. It appears that in some way he understood all of this. More light will be shed on why shortly.
[link to www.the-elite.net