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Secondary world is a term used by Tolkien to refer to a consistent, fictional world or setting, created by a man, also called subcreation, in contrast to the Reality, called Primary world. The world of Arda and generally the setting of the legendarium is Tolkien's Secondary World. His views regarding the "Secondary World" can be found in the essays The Monsters and the Critics.
Tolkien claimed that the author should respect his creation and grant it internal consistency, and let it obtain 'life' of its own. The tales should have several dimensions: geography, characters, languages, timeline, all being inter-dependent. The "scenery" should seem able to sustain the events and characters it hosts, and this would make the effect credible to the reader.
Tolkien had some mystical connection to sub-creation, believing that sub-creating helps us understand the Creation better, and of course the Creator (God). However this view has been his personal philosophy and doesn't reflect his religion as a Roman Catholic.
Students of Tolkien's works use the term "Primary" and "Secondary" to refer to two dimensions of the creation of Middle-earth. For example one can study Tolkien's languages being aware of both the Primary and Secondary factors.
The Secondary World history of the language, refers to the fictional history, that is etymological evolution of the language of the Elves, from Primitive Elvish until the First Age. There are many Secondary World versions for its history, each one belonging to the various levels of the myth.
Mysteries and gaps found anywhere in the legendarium, preferrably are discussed and solved Secondary World-wise.
These concepts are also known as "in-universe" and "out-of-universe" perspectives in other franchises.