Jones and screenwriter Ben Ripley wisely keep the explanation of how this process works to a minimum because either the explanation will make no sense, or it would take ten minutes of Basil Exposition to explain it. They even make the lack of explanation a minor plot point -- Gyllenhaal's character gets thwarted repeatedly by the scientist in charge of the project, who basically touches on a couple of points (parabolic calculus! quantum mechanics!) in a way that seems almost a parody of the Architect's ramblings in The Matrix Reloaded.
In any case, Gyllenhaal can be repeatedly sent into "the Source Code", the project's term for a weird mesh of time travel and mind-swapping. We're told repeatedly that the past can't actually be altered and that only information can be gathered to help the present. But is this true? And why can't Gyllenhaal's character remember how he came to join the project?
The obvious genre antecedents for Source Code are Groundhog Day and the Star Trek: TNG episode "Cause and Effect", with a little 12 Monkeys thrown in. Jones keeps the movie moving at a brisk clip, with the reiterations changing enough each time so that the movie becomes neither repetitive nor boring. Gyllenhaal is solid as the baffled soldier, Michelle is perky as a train passenger/love interest, and Jeffrey Wright and Vera Farmiga do nice work as the scientist and Captain running the project (dubbed 'Beleaguered Castle', a solitaire reference that plays out in the movie and also seems to allude to the importance of cards to the classic brainwashing thriller The Manchurian Candidate). Highly recommended.