Linnaean taxonomy can mean either of two related concepts:
The particular form of biological classification (taxonomy) set up by Carl Linnaeus, as set forth in his Systema Naturae (1735) and subsequent works. In the taxonomy of Linnaeus there are three kingdoms, divided into classes, and they, in turn, into lower ranks in a hierarchical order.
A term for rank-based classification of organisms, in general. That is, taxonomy in the traditional sense of the word: rank-based scientific classification. This term is especially used as opposed to cladistic systematics, which groups organisms into clades. It is attributed to Linnaeus, although he neither invented the concept of ranked classification (it goes back to Plato and Aristotle) nor gave it its present form. In fact, it does not have an exact present form, as "Linnaean taxonomy" as such does not really exist: it is a collective (abstracting) term for what actually are several separate fields, which use similar approaches.