"My people practically invented fixed points in time. Well, in fact, they did."
Fixed Points in Time (also known as Fixed Point in History) are an invention of the Doctor Who revival, used to explain that show's complicated and inconsistent dealing with how a time traveler can change fate. The original show had dealt with this as far back as The Aztecs, where it was suggested that time travel could not change the past. Other episodes dealt with it in different ways, and since classic Doctor Who could very quickly cycle between "involved discussions about theodicy" and "plastic spiders controlled by wires plot to take over the universe" the issue was never really explained.
In the revival series, it wasn't until the second episode of the fourth series, "The Fires of Pompeii" that the idea of Fixed Points in Time was revealed. This episode was written by our own James Moran, so I wish I could claim that it bubbled forth out of some long ago, esoteric discussion on here about time travel. But in a personal communication, he revealed to me that this particular concept was deigned from on high. Yet it works into the episode perfectly: let down in Pompeii, the Doctor admits that as a Time Lord he can feel places where time can be changed, and places where it can not. Pompeii is one of those places, and it turns out that the destruction of Pompeii must happen, and that the Doctor must be the one responsible.
The concept evolved. Whereas in "The Fires of Pompeii" it was just said that a Fixed Point in Time could not be undone, in the later special "The Waters of Mars", it is shown what happens when the Doctor does try to change a Fixed Point: history corrects him, tragically so. Still later, under Steven Moffat's direction, we learn that if someone really does manage to break a Fixed Point in Time, it starts unraveling the entire fabric of space and time, reducing the universe to atemporal chaos.
Like almost all of Doctor Who's shifting mythology, a the "Fixed Point in Time" can be used either to invite reflection, or to wave away something as "too complicated". Its meaning has evolved and shifted since it was first introduced, leading to more possibilities and a deeper meaning, but also perhaps (as so much in Doctor Who) becoming a convoluted excuse for things that don't make sense. It seems that the idea of the Fixed Point in Time is going to be given more of a showing in the 50th anniversary special, The Day of The Doctor, which reveals details of the end of The Last Great Time War.