What is Middle Earth in the middle of? Right Earth and Left Earth? Top Earth and Bottom Earth?
Middle Earth is caught between the Age of Men (i.e., now) and the ancient times and the great heroes of the days before. Likewise it is between the mythic lands of Valinor and… something. Maybe the Ocean.
Middle-Earth is not original to Tolkien, as most people assume, but derived (like many of his terms) from an Anglo-Saxon usage I don’t happen to recall, but which is equivalent to the Scandinavian Midgard – the world as being in the middle between Heaven/Asgard and Hel(l).
In Tolkien’s cosmology, it refers to specifically the Northwest of the Old World: northern and western Europe, as they existed prior to landform changes (some of which are detailed in the Silmarillion). It is distinguished from The East, beyond Rhun, where the two Blue Wizards went, and The Uttermost West, Aman, the Undying Lands ruled over by the Valar, where only Elves (and a few specially chosen mortals: Tuor, possibly Turin, Earendil and Elwing, Gimli, Frodo, and Sam) are permitted to go.
Polycarp’s right about Middle Earth as the place where the living dwell: between the dead below and the gods above. Tolkien’s interest in ‘Middle Earth’ (and specificially Earendil, one of the stars of the Silmarillion) was apparently sparked by a couplet from Crist by the Anglo-Saxon poet Cynwulf:
Eala Earendel engla beorhtast
Offer middangeard monnum sended.
(Hail Earendel, brightest of angels, sent to Men over middle-earth; cite here).