The narrator explains that the word “irie” has its roots in patois, the Jamaican dialect and in the Rastafari religion. Bob Marley, a Rastafarian, helped spread the word around the world. According to its original definition, the word means that one is "all right" with their god and the world—it connotes having a contented spirit.
By stepping out of the narrative to explain the history of the word “irie,” the narrator makes the case that people cannot escape from their histories. Just as all people are connected, people are also connected to their histories, no matter what.
To people who don't know all that, irie simply means that someone is "all right." Natasha wonders about some dictionary definitions that are marked obsolete, and thinks that the original definition of irie is gone. Samuel has begun using irie and other Jamaican slang for the first time since he moved to the US, and he acts happy now. Natasha can tell that it's just an act.
Natasha is clearly uncomfortable with change—in this case, the evolution of the word “irie.” This suggests that her love of science and math is also a love of unchanging mathematical rules and scientific laws. However, new scientific discoveries means the field is changing daily, so there is no way for Natasha to fully escape change.
Natasha believes that words should act like units of measure and not be allowed to change. She knows that if she leaves the US, all of her friendships will disappear. She'll feel like a stranger in Jamaica and wonders how long it'll take to pick up a Jamaican accent. The narrator muses that someday, Americans may use irie with perfect American accents, and the entire history of the word will be gone.
Considering Carl Sagan's assertion in the prologue, and the novel's assertion that people are always connected to their history, this final suggestion isn't entirely true. Even if one day, no one knows the word’s rich history anymore, that doesn't mean the history suddenly ceases to exist.