Fixed point in time

Fixed points in Time were points in time at which events could not change.

Definition
Fixed points were events and/or individuals who have such a long-standing impact on the timeline that no one, not even Time Lords, were allowed to interfere with their natural progression. The Doctor, while free to interfere in alien invasions and save planets in most cases, could not interfere/interact with these fixed points.

The opposite of fixed points was time being in flux. At these points time could change completely. It is unknown what happens to fixed points if the future is changed while time is in flux.

Notable fixed points
Jack Harkness became a fixed point in time after his rejuvenation by Rose Tyler (DW: The Parting of the Ways, Utopia)

The destruction of Pompeii by the Vesuvius volcano was a fixed point in time, caused by the Doctor. As well as its eruption, the deaths of most of the citizens of Pompeii were fixed. The Doctor, however, did manage to save one family. (DW: The Fires of Pompeii)

The death of explorer Adelaide Brooke marks one of the only times the Doctor intentionally interfered with a fixed point, under the rationale that, as the last surviving Time Lord, the Laws of Time were his to command. Ultimately, he was unable to prevent Brooke from committing suicide, thereby allowing the timeline to unfold, with only a few minor changes. (DW: The Waters of Mars)

The Doctor also interferred with a fixed point in time a short while before or after the previous event, by saving the life of Emily Winter, a film actress in 1920s-era Hollywood. He was put on trial by the Shadow Proclamation for this. (IDW: Fugitive)