Diegesis
In fiction, diegesis is that part of an entertainment which is obviously part of the narrative itself. In film and television, something is said to be diegetic when it is experienced by the characters. The term is seen with some frequency in literary criticism, as the concept dates back to the ancient Greek notions of drama. People who are more casual about the concept generally equate diegetic with in-universe and extra-diegetic with out-of-universe.
Examples from the DWU
Narrator
A diegetic narrator is a narrator who is part of the events of the piece, as was Gwen Cooper in Children of Earth: Day Five or Ian Chesterton on the VHS release of The Crusade. An extra-diegetic narrator is one who is not a part of the action, like Tom Baker on the VHS release of Shada, or Carole Ann Ford on the VHS release of The Reign of Terror.
Music
The term has great applicability with regard to an episode's soundtrack. Incdental or theme music is almost always extra-diegetic. The Eleventh Doctor can't hear "I Am the Doctor", but the audience can, every time the Doctor does something heroic. The Tenth Doctor didn't hear "Vale Decem" when he regenerated, but we did. No companion hears his or her theme, so they're all extra-diegetic.
Sometimes, though, songs are heard diegetically. John Smith and the Common Men provided the programme's introduction to diegetic music, as Susan was listening to their music in the first episode. "Ticket to Ride" followed the next year, and then came the programme's first original diegetic song, "The Ballad of the Last Chance Saloon". Other songs like "Paperback Writer" followed, though as the programme drifted away from Earth, so too did its opportunities for diegetic music.
The tradition has revived somewhat under Murray Gold, who's included a variety of original songs. Some, like "Song for Ten" and "Vale Decem" have been extra-diegetic, while others, like "Abigail's Song", "My Angel Put the Devil in Me" have been plainly heard by the characters.
Who cares?
The distinction between the diegetic and the out-of-universe may be lost on some. However, the editors of this wiki must take care to correctly note whether something is diegetic or not. The perspective with which we write articles or the categories in which we place them, changes greatly depending upon whether the article is about a diegetic or extra-diegetic element.
For instance, "Abigail's Song" is actually in category:songs, while "Vale Decem" belongs to category:incidental and theme music. We'd write "The Ballad of the Last Chance Saloon" initially in the past tense and then include a "behind the scenes" section at the bottom. But "Song for Ten" is entirely written from a real world perspective.