The conceptual bomb was a weapon developed by the Vess at the Factory. Planted inside an individual's brain, it made thought into reality and, subsequently, affected reality depending on the nature of the thought.
The Decayed Master planted a conceptual bomb in Bob Dovie's mind that would detonate upon him entering the Doctor's TARDIS on 23 November 1963 and believing the dimensional transcendence to be impossible. The bomb destroyed the TARDIS, removing it from existence so that the Doctor never chose that specific TARDIS and so never left Gallifrey. However, the First, Second and Third Doctors were able to disperse the destruction of the TARDIS across its whole timeline (Compared to bailing out a sinking ship by redistributing the water within it), thus limiting the rate of collapse so that they could alert their other selves to the danger. This timeline was eventually negated thanks to the Fifth Doctor travelling back to visit Bob Dovie in 1962 (Thus introducing him to the TARDIS before the conceptual bomb was planted so that he wouldn't immediately proclaim the TARDIS to be impossible), followed by the First Doctor deactivating the TARDIS component that would have drawn the ship to the bomb's location in the first place. (AUDIO: The Light at the End)