As previous posters have stated, "Salaam" basically means peace be with you in Arabic. It is most often spoken by Muslim cultures.
Certainly the significance of this scene is the seal of a friendship between Alai and Ender. Looking deeper however, one could examine it as a clue into Alai's past. One element that is ambiguous throughout the novel is the nationalities and backgrounds of the students at Battle School. When Dink mentions, "Nobody ever talks about home," he hits on something even the author (perhaps purposefully) left out. If this is a global war between aliens and humans, it has to be assumed that the students training for the battle are the best and brightest from around the globe.
There is a scene that was written in the original publication of Ender's Game which was later removed by the author (likely for the purpose of expanding the opportunity to teach the book in middle and high school classes), in which Ender and Alai have a quick and casual conversation in the Battle Room. Shen is referred to as a "slanty-eyed butt-wiggler" and Ender responds with, "Hey, we can't all be n*ggers." Nothing in the conversation is said with a tone of disrespect, rather, the casual nature of the entire thing makes it seem like the point was to give a brief glimpse into the nationalities of some of the other characters. From that conversation, Alai would most likely be assumed to be an African American (another line says "my great grandfather would have sold him first," in reference to Alai's grandfather being a slave).
In light of this information, Alai's use of the word "salaam" might be less of a reference to his heritage, and likely more of a reference to some sort of religious belief. Whatever the purpose, the taboo subjects of life before battle school and religion in general certainly heighten the sacredness of this moment for Ender.