The world containing J.R.R. Tolkien’s Middle-earth is called Arda.
In Tolkien’s legendarium, Arda is the realm created for the Children of Ilúvatar, including the lands and seas where the major stories take place. Middle-earth is not the name of the entire universe or world; it is a major region of Arda, especially the setting of The Hobbit and The Lord of the Rings.
Arda exists within Eä, the wider universe brought into being through the Music of the Ainur. Aman is a continent or realm associated with the Valar, while Valinor is the land in Aman where many of the Valar dwell. These related names are frequent sources of confusion.
The shape and geography of Arda changed across Tolkien’s imagined history. The destruction of Númenor, for example, was connected with a major reshaping of the world. Thus, “Arda” is the precise answer when the question asks for the world rather than a continent, kingdom, or city.