A time-aware faction or civilisation [source needed] was one with some knowledge, if not influence over time-active powers, which could, for example understand the significance of the Last Great Time War even if they had no part to play in it.
Aside from certain select organisations, humans did not even partially grasp the significance of the various temporal factions for much of their history. By approximately the 51st century, humans had some awareness of Time Lords, though representatives of that species, such as Sabalom Glitz tended to think of them as almost magical, at the same time not seeming to take them entirely seriously. (TV: The Mysterious Planet) The 51st century Time Agency has some knowledge of Time Lords and the Time War, with Time Agent Jack Harkness regarding it as "just a legend". (TV: The Parting of the Ways)
By contrast, five billion years later, Jabe, a member of another, Earth-derived species, the Forest of Cheem, seemed cognisant of the Time War and the loss created by it, in apparent contrast to the humans of that era. (TV: The End of the World) In the Humanian Era, Lassar of the Krillitane had knowledge of the Time Lords and their extinction (TV: School Reunion), as did the Sontarans (TV: The Sontaran Stratagem) and Rosanna Calvierri. (TV: The Vampires of Venice)