Living Time is the concept of the Universe being alive. Not like an organic organism like you or I who are acutely aware of our own existence and capable of manipulating what we please. It's hard to describe exactly in what way. The concept of Living Time is backed by some legitimacy, as Forerunners especially gifted at picking up the nuances of Living Time, like the Librarian, were capable of making predictions a many great years into the future. It's what allowed her to be such an effective planner. Curiously enough, when the Flood onslaught begone, Living Time appeared to turn against the Forerunners. It was described that the stars itself burned with a harsher light, that seemed to glare at the Forerunners. Which interestingly enough coincides with the Precursors' wrath. As such I theorize the Precursors are the physical manifestation of Living Time.