Here's what I think happened:
Colter (a pilot from Afghanistan) wakes up in Sean's body - alive, well, and awake - on a train approaching Chicago. He's sitting across from Christina. He doesn't get how and why she knows him, thinks he, she, and/or everyone around him is crazy. Before too long - 8 minutes, to be exact - the train blows up and kills everyone.
We soon learn that Colter is really now on a mission - to find out who set the bomb that blew up the train. His mentality is able to go back into Colter's body on that train, via a new process known as "source code". He can be sent back for 8-minutes, to the same time, as many times as necessary - though it takes an emotional toll on him, as noticed by Colleen Goodwin (his direct supervisor, who is concerned about this) and Dr. Rutledge (head of the project, who cares only about this mission). It is this going back as many times as necessary that has led to some characterizations of Source Code as Quantum Leap meets Groundhog Day. Source Code also has some echoes of 12 Monkeys - same gritty feel in parts (just like Fringe) - but it really has little in common with time travel.
We're eventually told by Rutledge that the source code creates an alternate reality - Colter in Sean's body on the train - and the plan is that if Colter can get the name of the bomber to Goodwin and Rutledge, they can use this to stop a much worse potential explosion, which we learn is a dirty bomb that would take out a big piece of Chicago.
It takes Colter most of the movie to get the bomber's name. By this time, he's fallen for Christina, and wants to save her, and, while he's at it, all the people on the train. Rutledge insists that can't happen - the source code is about influencing the future (stopping the big explosion in Chicago) not about changing the past (stopping the bomb on the train). After Rutledge gets the name of the bomber, which leads to his being stopped before he gets to Chicago, Rutledge wants to erase Colter's memories of this and send him another mission. Goodwin, who has more empathy for Colter, defies Rutledge and sends Colter back one more time - presumably so he can at least die feeling somewhat fulfilled, by calling his father (who thinks his son Colter was killed in Afghanistan), being with Christina one last 8-minute time, and saving her and everyone on the train by defusing the bomb.
Now we get into somewhat speculative territory. Here's what I think happened on that score:
On this last mission to the train, Colter has indeed stopped the bomb from going off on the train - in that alternate reality. This apparently allows that reality to continue, not only with all the original passengers on the train, but with Colter (in Sean's body), so that Christina and Colter live happily ever after, beginning with their kiss on the train that was not followed by the train exploding.
In our reality, Rutledge is furious that Goodwin defied him. But in the alternate reality - which is now continuing beyond 8 minutes, because Colter stopped the train from exploding - Colter is able to send Goodwin a text that shows that he is not only alive in some sense in this alternate reality lab, but that another reality (our reality) had successfully sent him back to this reality - that is, the reality in which Colter was sent back numerous times from our reality - if you're still with me.
So, all in all, a pretty good story, as I said, but maybe having more in common with Fringe than any time travel story, and a bit short on clear, scientific or pseudo-scientific explanation.
And also a little short on at least one ethical issue: what happened to Sean in the alternate reality? True, he would have died anyway, without Colter's intervention. But now Christina thinks she's with Sean, when in "fact" she's with Colter, because in this "happy" ending Sean no longer exists.
Hey, if you like science fiction movies that are really about time travel, see Back to the Future, 12 Monkeys, or Deja Vu. Or check out this low-budget 2002 short movie by Jay Kensinger, adapted from my 1995 novelette published in Analog Science Fiction and Fact Magazine ... "The Chronology Protection Case" ....