Interstitial time, also referred to as interstitial space, the interstitial gap, the interstix, and interstitiality, was a theoretical zone of nullity, "the gap between now and now." Literally, outside of reality.
This interstitial gap was an envelope of non-space, non-time, underlying the "real" universe and surrounding and separating every space-time event. It had a kaleidoscopic appearance that was infinity, with sharp and precise colours and colourlessness that floated and merged together in a whirlpool, but there were also lots of empty white spaces. Perspective was fluid to a person observing this; if they ran, the space stretched into a tunnel. There was also a pseudo-ground to walk on. The interstix had some form of "sentience," responding to or mentally attacking individuals with experiences that their minds made real. Whether or not individuals trapped in the gap could age or starve was unknown as the gap was "no-time."
Interstitial space was also composed of "the building blocks of reality." Gabriel and Tanith actually made Harry Truman's body out of the "stuff of chaos" of interstitial space. (PROSE: Falls the Shadow)
The Master, under the alias of "Carl Thascales" at Cambridge, researched and experimented with interstitial time using TOMTIT. Though his ultimate goal was to access the Crystal of Kronos to release Kronos, he was able to slow down time around the area and move solid objects through the interstices of reality, taking advantage of the granularity of space-time. (TV: The Time Monster, PROSE: The Quantum Archangel)
Jeremy Winterdawn, using Thascales' notes in 1994, continued exploring the concept of interstitial time through use of the metahedron. This actually allowed him and the Seventh Doctor to enter the interstitial gap, where they became trapped and were eventually brought back by the Grey Man. (PROSE: Falls the Shadow)