The battle of Battle of the Pelennor Fields happens at the exact time Sam rescues Frodo from Cirith Ungol on March 15. In "The Land of Shadow," Sam says:
‘If only the Lady could see us or hear us, I’d say to her: "Your Ladyship, all we want is light and water: just clean water and plain daylight, better than any jewels, begging your pardon."’
They keep walking and a few moments later:
‘Look at it, Mr. Frodo!’ said Sam. ‘Look at it! The wind’s changed. Something’s happening. He’s not having it all his own way. His darkness is breaking up out in the world there. I wish I could see what is going on!’
It was the morning of the fifteenth of March, and over the Vale of Anduin the Sun was rising above the eastern shadow, and the south-west wind was blowing. Théoden lay dying on the Pelennor Fields.
Sam was in possession of the Phial of Galadriel, which has powers of light, while making his wish. This lines up at the turning point of the Siege of Gondor, where The Darkness fails, which filled the hearts of men with dread, and only Gandalf and the Prince Imrahil could counter it momentarily. In the end of "The Ride of the Rohirrim" and the start of "The Battle of the Pelennor Fields" we see:
For morning came, morning and a wind from the sea; and darkness was removed, and the hosts of Mordor wailed, and terror took them, and they fled, and died, and the hoofs of wrath rode over them.
The darkness was breaking too soon, before the date that his Master had set for it: fortune had betrayed him for the moment, and the world had turned against him; victory was slipping from his grasp even as he stretched out his hand to seize it.
Does Tolkien ever explain why The Darkness fails?
The books leads me to conclude that it was Galadriel's power that dispels The Darkness and allows the victory of the Siege of Gondor.
Edit: Ok people have been getting tunnel vision on "Well actually Galadriel actually did not created..." instead of the more important question of why The Darkness goes away and if Tolkien left any clues. Sam and the Phial are the only ones shown that are related to The Darkness going away, this is why I put the theory forward.