what is linnaean classification?

Carl Linneus was the biologist who developed the system of classification for living things that is not unlike what we still use today.

It is basically a branching system of choices. From 'all living things' it branches into major kingdoms like plant or animal, and then those branch into smaller and smaller groups until you get a unique species at the very bottom. If you start at the top and follow the branches down, you can tell exactly what any creature you're looking at happens to be (or even if it is a completely new creature).

It was Linnaeus who also developed the tradition of referring to a species by just its genus and species name instead of the whole classification. So, for example, humans are homo sapiens and wolves are canis lupus.

These were such great ideas that they were very readily adopted by scientists around the world. Suddenly they had a great system to organize and talk about things in such a way that everyone knew what they were talking about. Of course, what we use today is far more complicated with more tiers and different organization than what Linnaeus came up with... but at its core it still follows the same prinicples.

Hope that helps!

Carolus Linneaus was the first to classify organisms based on phenotypes (observable traits). His form of classification has been the default form of classification for a couple of centuries. However, with the advent of genotyping and preparing genomes for all known organisms, biologists have found certain similarities in the DNA of organisms that were once thought to be too distantly related to be classified in the same group.

Linnaean classification is, therefore, being challenged and adusted.

The creationist scientist, Carolus Linnaeus (1707–1778), the founder of the science of taxonomy, tried to determine the created kinds. He defined a ‘species’ as a group of organisms that could interbreed among themselves, but not with another group, akin to the Genesis concept.
http://www.creationontheweb.com/content/view/271/

Carolus Linnaeus (1707–1778) was the creationist scientist and the founder of the science of taxonomy who “established the two-part naming system of genus and species.” “There can be one or many species in a genus, so genus is a higher level of classification. Linnaeus also developed the idea of grouping genera (plural of genus) within higher groupings he called orders, and orders within classes.” “Later, other levels of classification were added so that today we have species, genus, family, order, class, phylum and kingdom. Sometimes other levels are added, such as subfamily and subphylum.”