A prophecy was a statement made by a prophet, which foretold some future event, such as the appearance of a significant individual or a great crisis.
In 2152, while keeping an all-night vigil for his ill dog Porthos, Jonathan Archer dreamed that Porthos had died. After waking and telling Doctor Phlox this, the doctor replied that he hoped Archer's dream wasn't prophetic. (ENT: "A Night in Sickbay")
In 2153, after watching the horror film Frankenstein, T'Pol commented that she found the villagers' reaction to Frankenstein's monster to be prophetic, comparing it to the way Humans reacted after Vulcans first landed on the Earth. (ENT: "Horizon")
In 2267, Marplon was pleased to see the members of USS Enterprise's landing party, or the Archons, as he called them. When Spock corrected his assumption that they belonged to such a group, Marplon insisted that nevertheless, they were the fulfillment of prophecy. Later, James T. Kirk asked for more information on Landru. Marplon attempted to explain the details of the prophecy, but Kirk interrupted him, uninterested in what the prophecy said. (TOS: "The Return of the Archons")
In 2371, Chakotay expressed his concerns to Captain Kathryn Janeway about needing to establish a policy on fraternization on USS Voyager, given the starship's being far from home in the Delta Quadrant. Later, woried about Kes as her window for elogium was rapidly closing, Janeway called the first officer's concerns prophetic. (VOY: "Elogium")