A continuity bomb was a Dalek weapon developed during the Last Great Time War. The bomb was programmed to target one individual, altering one event in their main timeline and changing their "continuity" to one of the billions of alternate timelines they existed in. Ideally, the end result was to create Dalek Slaves, as was the demonstrated effect in a possible timeline of the War Doctor. Individuals who would not second guess their decisions and were noble in their actions had no useful alternate timelines to the continuity bomb. The Ninth Doctor was considered to be such an individual, as he was never "anything less than fantastic" in every timeline he existed in.
The Tenth, Eleventh and Twelfth Doctors found one, but were unable to disarm it. However, since all three of them were present when the blast went off, they were left shifting between three separate timelines, one for each Doctor, where each made a decision which negatively affected them and the universe.
This was revealed to be part of a complex plan by the alternate Twelfth Doctor that was witnessed when the bomb went off as he sought to ensure his own existence, creating the illusion that his future was the least "damaging" of the three possibilities when in reality he intended to conquer the universe. However, the Doctors were able to defeat his plan when the Tenth Doctor's companion Gabby Gonzalez went back in time to warn the others, allowing them to gather equipment in the Eleventh Doctor's timeline to defeat the future Twelfth. (COMIC: Four Doctors)