I was looking at the map of Middle-Earth and it made me wonder. Does Middle-Earth refer to the time frame in which the LOTR stories took place, or does it refer to the area in which the LOTR tales unfold? To help clarify what I'm asking: Is the rest of Tolkiens' unmapped world Middle-Earth too, or is Middle-Earth the era?
Middle-earth is the name for the parts of the world in Tolkien's universe where men lived. It was based on the Old English/Norse term "Middangeard" as used, for example, in Beowulf. The term "middle" here comes from the Norse idea of nine connected worlds, of which men lived on the one in the center. This distinguishes Middle-earth from, for example, Valinor where the immortal Valar lived.
Tolkien's Middle-earth includes other places that are not on his maps of Middle-earth that are still part of that region, but there are also unmapped areas that are outside of Middle-earth. Tolkien described Middle-earth as basically being surrounded on all sides by ocean, so anything that was "across the seas" would be somewhere else.
In practice, Tolkien fans often just use "Middle-earth" to mean the setting of the novels, without being too concerned with where it stops and starts
Middle-Earth is the world as a whole, minus those parts removed from the world by Eru - the Undying Lands. This includes the unseen east and south, and could also be used to refer to our world if accepting Tolkien's intent of LotR as a mythology for our world.
Middle-earth is just archaic English for oκονμένη, the inhabited world of men. It lay then as it does. In fact just as it does, round and inescapable.
From Letter #151.
It is complicated: it is certainly a time period, but it is also a position. In addition, it is certainly related to Midgard of Germanic cosmology.
In his conception, the author had the world flat (flat-ish and boat shaped), and the middle-earth of the Hobbit and LotR was pretty much in the middle (north middle). At one point, the world is changed and becomes round, and the middle portion become the farthest west, since the closer bit was lost to the sea (the western shore of the later maps was actually east of the shore of the earlier maps).
I think that Middle-Earth refers to the way the world looked during the age of men. So that would make it both spatial and temporal in reference.
"Middle-earth is just archaic English for oκονμένη, the inhabited world of men."
I think this quote actually supports the idea of a temporal definition of Middle-Earth. For instance, The Shire is not so much physically inhabited by men, but it does exist within Middle-Earth in some sense.