Tolkien's most widely read works, The Hobbit and The Lord of the Rings, take place entirely in Middle-earth, and Middle-earth has also become a short-hand to refer to the legendarium and Tolkien's fictional take on the world.
Because the Sun, Moon, stars, and other objects orbited the planet in the cosmology of Middle-earth they were considered part of Arda, leading to Arda sometimes being called the 'Solar System' of Middle-earth. The term for the Earth itself, excluding these celestial bodies, was Ambar or Imbar.
See Middle-earth for the main article about Tolkien's fictional universe
In the Second Age, Númenor was raised in the Great Sea for the Edain. This island existed through most of the Second Age, but was destroyed as a result of the pride of the Númenórean people in defying the Ban of the Valar and sailing to Aman in the west.
After the destruction of Númenor, Arda was made round. Aman (The Undying Lands) was taken out of the world into an alien dimension, and could only be reached by the Elves, following the straight road that was granted to them. As Aman was taken away from Arda, new lands and continents were created.