In this wiki, a hyperverse is defined as a reality of a higher dimensional order than our own likely 11-dimensional multiverse. In other words, any 12-dimensional reality, realm, etc. or above is referred to as a "hyperverse" for organisational purposes, in order to differentiate concepts of this nature from standard or complex multiverse definitions.
More specifically, 12-dimensional structures vastly exceed and transcend 11-dimensional ones, but are still loosely related to them, and are the minimum requirement for a hyperverse classification or "low hyperverse". Otherwise, any uni/multiverse of a finite number of spatio-temporal dimensions greater than 12 are all classified as "hyperverses" within this wiki.
The mathematical concept of a "Hilbert Space" is an infinite-dimensional analog of Euclidean space. Infinite-dimensional spaces of both higher and lower magnitudes are high hyperversal. Simply, this is an infinite space in the literal sense. Any structure infinitely superior to an infinite-dimensional hyperverse is only an infinite dimensional structure of a greater magnitude.
The term that we are specifically using for this wiki is likely not found in any notable work of fiction. In simple cases, the universe or multiverse can be described as being 12-dimensional or higher, and thus qualify as a "hyperverse" by our standards.
However, the term used in this wiki is not defined the same outside of this wiki. "Hyperverse" in this case comes from two words: "Hyper", which is used in mathematics to designate higher-dimensional space, and something extreme, above or beyond the usual level. As well as "verse" as a short for "universe". So it is intended as a description of a superior higher-dimensional existence, beyond conventional reality.
In other words, a hyperverse and multiverse in fiction are the same thing, however a different term was coined in order to not conflict with real-world definitions, theories, and interpretations of a multiverse, more specifically, M-Theory, String Theory, and Brane Cosmology.