A conceptual entity was a being or weapon (sometimes both) engineered to be only a concept, with no actual physical substance from existing only as an idea.
Conceptual entities were "hostile ideas" that could bypass matter altogether and instead give themselves structure inside the meanings of things, using the network of understanding or "the topology of comprehension" to change the very meaning of objects and ideas. This in effect caused conceptual entities to worm themselves into culture itself. The Celestis compared them to computer viruses: corrupting and rewriting data, but inside ideas rather than computers. (PROSE: The Book of the War)
The Time Lords were known to have designed and possessed multiple different Gallifreyan conceptual entities and weapons in the past. A TARDIS was capable of detecting conceptual entities, so long as they were actively scanning for them. (PROSE: Alien Bodies)
The Celestial Intervention Agency became the conceptual entities called the Celestis after turning themselves into completely conceptual beings to avoid being destroyed by the War in Heaven, removing themselves from history so that while they never physically existed, the "idea" of them survived. (PROSE: Alien Bodies) The Celestis later became experts in the creation and engineering of other conceptual entities such as gargoyles, anarchitects, and shifts, which the Enemy weaponised in the War. (PROSE: The Book of the War)
The Celestis' realm of Mictlan was noted to be uniquely constructed as an entire conceptual "ecosystem" instead of a single entity. (PROSE: The Book of the War)
The Shan'tee and the Nocturne species are conceptual beings made out of living sound. (COMIC: The Singer Not the Song)