As a linguist, Tolkien took “Middle-earth” from earlier writings and it is synonomous with Midgard, Middenheim, etc. in Germanic (Nordic) mythology. Although Tolien was not always consistent with his use of “Middle-earth”, He generally used the term to refer to the main continent of Arda. In Tolien’s mythology, Arda (“Earth”) was created flat. So the land was the middle of Arda between the sky and the deep sea. It was also the main continent between the land of the gods (Powers) in the West (Valinor) and the eastern edge of the world where the elves originally awoken. Only at the end of the Second Age with the destruction of Numenor was Arda made round (and Valinor removed from the confines of the physical world). After that, “Middle-earth” primarily is used to describe the main continent of the world in which lay Arnor, Gondor, Mirkwood, and Mordor.
Sorry, Tolkien geek here. 🙂 For anyone who has read only The Hobbit and the LOtR trilogy, I highly recommend reading The Silmarilion and the Book of Lost Tales (Vol. 1 and 2). The additional back story is incredible and you can really see how Tolkien spent his life (from the early 1910’s until his death in 1972) working and re-working the mythology and tales of Middle-earth.