Miracles were unusual but beneficial phenomena usually attributed to supernatural intervention. In the words of the Eleventh Doctor:
The universe is big. It's vast and complicated and ridiculous, and sometimes, very rarely, impossible things just happen and we call them miracles, and that's the theory.
The Latter-Day Pantheon used their reality-warping abilities to perform many miracles in New York City in 1965, leading to many believing them to be gods. (PROSE: Salvation)
Lolem believed that the disappearance of the Second Doctor and Ramo was the miracle of Amdo having eaten them. (TV: The Underwater Menace)
The Eleventh Doctor initially attributed Rory Williams's resurrection to a miracle. (TV: The Pandorica Opens)
The sudden end of death on Earth in 2011 became known as Miracle Day. (TV: The New World) When Oswald Danes saw Jack Harkness come back to life after Miracle Day ended, he thought it was a miracle. (TV: The Blood Line)
The inhabitants of Detrios named their new source of light and heat the Miracle. (PROSE: Head Games)
When Alistair Gryffen found that the chess room in Gryffen Manor was remarkably tidied up, he called it a "minor miracle". (TV: Black Hunger)