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 conquer Aman and obtain immortality from the Valar, they laid down their guardianship of the world and called upon Eru Ilúvatar and the world was changed forever. The land of Aman and the island of Tol Eressëa were removed from the Circles of the World forever and could only reached by the elves sailing West following the Straight Road.
Númenor itself was destroyed and fell beneath the waves of the tumultuous sea. 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.
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 their way back to where they started. This set the stage for the dominion Men that would begin in earnest after the War of the Ring.