The prophecy, which was overheard by Severus Snape, stated:
"The one with the power to vanquish the Dark Lord approaches... born to those who have thrice defied him, born as the seventh month dies... and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not... and either must live or die at the hand of the other, for neither can live while the other survives... the one with the power to vanquish the Dark Lord will be born as the seventh month dies..."
It's important to note that the prophecy itself was ambiguous and could have applied to several children born at that time. However, Voldemort, fixated on the threat it posed, chose Harry as the one it referred to, leading to the events of the books.