Rank refers to the relative position, value, worth, complexity, power, level etc. of an object.
Rank refers to the relative position, value, worth, complexity, power, importance, authority, level etc. of a person or object (source).
From Wikipedia:
In computer programming, rank with no further specifications is usually a synonym for (or refers to) "number of dimensions"; thus, a bi-dimensional array has rank two, a three-dimensional array has rank three and so on. Strictly, no formal definition can be provided which applies to every programming language, since each of them has its own concepts, semantics and terminology; the term may not even be applicable or, to the contrary, applied with a very specific meaning in the context of a given language.