The key to this is an idea called linguistic co-ordination, in which speakers naturally copy the style of their interlocutors. Human behaviour experts have long studied the way individuals can copy the body language or tone of voice of their peers, some have even studied how this effect reveals the power differences between members of the group.
Now Kleinberg and so say the same thing happens with language style. They focus on the way that interlocutors copy each other’s use of certain types of words in sentences. In particular, they look at functional words that provide a grammatical framework for sentences but lack much meaning in themselves (the bold words in this sentence, for example). Functional words fall into categories such as articles, auxiliary verbs, conjunctions, high-frequency adverbs and so on.
The question that Kleinberg and co ask is this: given that one person uses a certain type of functional word in a sentence, what is the chance that the responder also uses it?