The Change of the World refers to the event when Arda became a round sphere instead of the flat surface that it had been for tens of thousands of years.
After Ar-Pharazôn broke the Ban of the Valar by sending an army to Aman to conquer the Valar and obtain immortality from them, the Valar laid down their guardianship of the world and called upon Eru Ilúvatar, who responded with a great cataclysm that forever changed the world.
Ar-Pharazôn's great fleet was sunk and he and his soldiers were buried under mounts of falling earth and imprisoned in the Caves of the Forgotten until the end of the world. Númenor itself was destroyed and fell beneath the waves of the tumultuous sea. The land of Aman and the island of Tol Eressëa were removed from the Circles of the World forever and could be reached only by the Elves sailing West, following the Straight Road.
The world from then on was round as the seas and the lands bent back upon themselves. Afterwards, the mariners of mankind who attempted to sail westwards found only the New Lands and eventually made their way back to where they started. This set the stage for the dominion of Men that would begin in earnest after the War of the Ring.