A point of divergence was an event, however small, that caused one timeline to split off from another, forming a new quantum reality in the multiverse.
According to multiverse theory, new realities were being born every moment, as every choice that could be made, would be made, in an alternate state of existence. These "choice points" were a natural form of "divergence" that did not go against the natural forces at work in the multiverse.
However, more significant points of divergence tended to revolve around the choices effecting the outcomes of important historical events, especially those at the epicenter of a temporal event. Most "linked" realities, including those known as mirror universes, were theorized to be born from these significant points of divergence.
As an example, the divergence point between the Prime reality and the Kelvin timeline happened when the Narada traveled from 2387 to 2233 and drastically alerted the life of James T. Kirk, an historical figure of immense temporal significance. The resulting stress to the space-time continuum caused the new reality to branch off, with effects preceding cause, altering the nature of the new universe into the distant past, as well as the future. In that instance, had the event not been so significant, the effects may not have been as profound; for example, had the Narada appeared, but not engaged the Kelvin, an alteration to history would have occurred, but the "flow" of the "river of time" would have soon course-corrected because the change would have been relatively minor.
Other points of divergence are more nebulous, but can still be traced to the outcome of an event, if not the specific moment or decision point. For instance, while the Borg, or something like them, are considered to be a "quantum inevitability," their nature may be fundamentally different in various quantum realities, because of divergence points. In the First Splinter timeline, the Borg arose from the Caeliar, partially due to temporal events involving the starship Columbia (NX-02). While the Borg still exist in other versions of reality, their specific origin is different in many of those, some in small ways, some in every way, with near-infinite variety.