Spoilers were things one individual knew about another's personal future. River Song particularly favoured the term, and used it to warn the Tenth (TV: Silence in the Library) and Eleventh Doctor (TV: The Name of the Doctor) when they asked questions that she couldn't answer without revealing details about their futures.
The Tenth Doctor also used the term to refer to reading books from Donna Noble's future; the Doctor taking a 51st century book away from Donna so as not to read ahead and "spoil all the surprises". Donna questioned if travelling in time with the Doctor was "one big spoiler". The Doctor responded that he tried to keep her away from major plot developments, which he also said he seemed to be "very bad" at. (TV: Silence in the Library)
The Eleventh Doctor used this to the Tenth Doctor when he asked him how he could forget after 400 years how many children there were on Gallifrey the day they remembered the War Doctor destroying the planet. (TV: The Day of the Doctor)
Of course, neither the Doctor nor River was the originator of the term. The Doctor had certainly heard and used it long before meeting River. While being tortured by a member of Faction Paradox in San Francisco, the Eighth Doctor strongly cautioned him against revealing any spoilers. (PROSE: Unnatural History) The Tenth Doctor also said the term to Donna shortly before River's archaeological expedition arrived on the Library. (TV: Silence in the Library)
Other companions besides River also knew the term. Fitz Kreiner once wrote a song called "Contains Spoilers" which he assured his audience did indeed contain spoilers. (PROSE: The Gallifrey Chronicles)
Alternate meanings Edit
In the newspaper trade, spoilers were a marketing tactic. According to James Stevens, when one newspaper scored an exclusive in an early edition, competing newspapers would spoil their competitors by printing the substance of the scoop in an edition that came out mere hours later. (PROSE: Who Killed Kennedy)
In television, a spoiler was any information about an episode that had yet to be broadcast. KWJM3 broadcast an hour-long trailer for their upcoming fall season, something that was full of spoilers about upcoming content. (PROSE: Synthespians™)