A time demon was a creature of the Time Vortex. The Sixth Doctor found the name ridiculous, considering it a "neverwas", an "after-thought with malice a forethought", and an "idea that got above its station", and proposing the name "time louse" instead. Like other temporal predators, it feasted on the chaos created by manipulating time.
One such creature possessed Stapleton Petherbridge and created a pocket of cauterised time around Pease Pottage in 1987. Using Mel Bush's incredible ability for "total recall" to manipulate time as well as two versions of the TARDIS, it planned to enter the real universe.
The demon claimed the Doctor's TARDIS had passed through it many times, though whether this was metaphorical or literal is unclear.