It was a bit confusing, but here's my take on it (necessarily a bit lengthy).
There were flashbacks throughout the episode (in which Reese was bearded) showing that Reese's ex-girlfriend, Jessica's husband Peter had staged a car accident husband to cover the fact that he had killed her by snapping her neck when she hit her head on a table during a fight,
It becomes clear Finch and Reese came together too late to save Jessica, as we see Reese brush past Finch, who is in a wheelchair in the hospital Jessica was brought to,
Later, once Reese had ended his life on the streets and was working for Finch, he finds out the truth, and kills the husband.
The connection of Reese to this killing is found by FBI man Donnelly, and he enlists Carter's help to check out the lead, but she suppresses a photo of Reese with Jessica, which she uses to obtain his special forces record (she later shreds this, but keeps the photo).
The case being worked by Finch and Carter relates to a deputy US Marshal, Jennings, who has framed his wife, who is on the run under assumed names, to keep her within his grasp. reese spirits her away from Jennings, but she is recaptured trying to flee NY City, and Jennings abducts her. Reese follows using more of Finch's technical wizardry.
Carter is afraid he will kill Jennings, due to parallels with Jessica's story, but at the end she receives a call from a prison warden in Mexico informing her that an American is now serving an imprisonment for drug dealing, after US Marshal Jennings, confirmed as a "a man in a suit", i.e. Reese, turned him (Jennings) in.