Both the newspaper article that Meursault finds in his prison cell and the play Le Malentendu / The Misunderstanding are inspired by a newspaper article that Camus cut out off an Algerian newspaper in June 1935, which reported a real event (B. Pingaud: L'Étranger d'Albert Camus. Gallimard, 1992; page 145). The story's significance becomes clear when we compare the traveller's attitude towards truthfulness with Meursault's.
When Meursault talks to his lawyer for the first time after his arrest, the lawyer tells him that witnesses had described him as insensitive at his mother's funeral and that this might be used against him during the murder trial. The lawyer asks him whether he would be willing to say that he had tried to control his emotions at the funeral ("dire que ce jour-là j'avais dominé mes sentiments"), Meursault responds, "No, because it would be untrue" ("Non, parce que c'est faux"; emphasis added). The lawyer is not pleased by this answer.
The rest of the narrative is also constructed in a way that suggest that Meursault is put on trial for being committed to the truth, as opposed to agreeing to follow the rules of the game by lying when necessary. However, in order to present Meursault as someone whom society wants to eliminate for his commitment to truth, he also needs to be portrayed as an "innocent murderer". There are two important ways in which the novel achieves this. First, the killing of the Arab (end of Part One, chapter VI) is described as a unfortunate accident (Meursault is half-blinded by the reflection of the sun on the Arab's knife blade, and just at that moment, the sweat that had gathered over and in his eyebrows rushes down into his eyes, so he pulls the trigger). In the second part of the novel, the Arab is never mentioned again (except once, during the trial; questions about the killing are otherwise about "the shots" or "the body"). The prosecution asks him why he fired five shots (Meursault says it was the sun) but the trial focuses mostly on Maursault's behaviour at his mother's funeral, what he had done the day after (go swimming with a woman he likes, then go to the cinema and spend the night with her) and what he had done for Raymond Sintès, who is suspected of being a pimp.
The behaviour of the traveller from the newspaper article contrast with Meursault in that he is willing to play games: by not revealing who he is to his own mother and sister, he shows that he is willing to pretend to be different that he really is. He pretends to be a stranger. (Ironically, this makes him another stranger inside a story discovered inside a novel about the stranger.) Meursault comments: "I thought that the traveller had deserved it to some extent and that you should never play games" ("ju trouvais que le voyageur l'avait un peu mérité et qu'il ne faut jamais jouer").
The conclusion from the comparison between Meursault and the traveller is rather depressing: if you consistently stick to the truth, society will try to get rid of you; if you play games, those may also end deadly. There is no way out. And this impression of having no way out is present in other passages in the novel. At the end of Part One, Chapter 1, the nurse who accompanies the funeral procession comments on the heat:
"If we walk slowly, we risk risk getting sunstroke. But if we walk too fast, we work up a sweat and catch a chill inside the church." She was right. There was no way out.
(Note that the French text uses the indefinite pronoun "on", which may be translated as "one" (very formal when compared to the novel's overall style), "we" (which is plausible in this specific context) or "you" (as some translators have done).)
Meursault's struggle with the heat leading up to the killing (the end of Part One, chapter VI) is also reminiscent of this concept. When Meursault sets out to the rock where the "Arabs" had been earlier, he feels as if the heat were pressing against him, but once he is close to the Arab, he feels as is the heat is pressing him forward, as if preventing him from turning around and letting go of the earlier incident. Again, there seems to be no way out.