The fictional world commonly called Middle-earth in J.R.R. Tolkien’s writings is Arda.
Arda is the larger world created by Tolkien for the mythology of The Silmarillion and related writings. Middle-earth is a major region of Arda, not the name of the entire world. This distinction is a frequent source of confusion in summaries of Tolkien’s legendarium.
Arda includes the lands of Middle-earth and, at different stages of the mythology, regions such as Aman. Its history begins with the shaping of the world by the Valar under the authority of Eru Ilúvatar.
Tolkien’s world changes over vast periods, including the destruction or reshaping of lands and the changing form of the seas. The stories of The Hobbit and The Lord of the Rings take place in Middle-earth during the later part of this long history.