Everyone knows that you need to use simple words when talking to little kids, so 'big' words like classification, clustering, facets and hierarchy (a distasteful term which even some grownups find difficult to spell) are out. So let's start with a tree. Imagine a tree. What's a tree really? You could say that a tree is like a 'parent', and it has 'children': A trunk that splits into several big branches that in turn split into smaller twigs that split into even smaller twigs where leaves sprout and fruit grow. If the child is really curious, you can talk about the parts of the tree that only moles could see if moles could see: The taproot which is the main root that grows vertically into the ground
So. is taxonomy like a tree? wait, wait... because there is another way to describe a tree: The bole is the part of the tree between the ground and the first branch, the crown which is the part of the tree from the first branch to the top, and the top which is the highest part of the tree.
And...a tree is a plant and there are all kinds of trees and here are just a few: Redwood, Ash, Fir, Spruce, Sequoia. There are banana trees, apple trees, orange trees and how exactly is a Sequoia related to and Avocado tree? And even more: A collection of trees can form a forest, grove, garden, or park which by themselves are not just collections of trees but wider concepts. So of course, the development of a taxonomy involves research, and among other things, one can find that for many domains, especially in life sciences, law, government and many others, it is possible to start the process with an existing taxonomy, see for example the taxonomywarehouse.
It is clear that the scope of concepts in the world is endless due to the Human instinct to stereotype and classify, first explored by Aristotle, or at least - this is our first written record of an arrangement to classes, subclasses and so on, as means to understand our world. But if so, lets keep in mind that children must have an inherent understanding of classification, and by extenuation, of taxonomy. It is only a matter of vocabulary then.
Taxonomy is a communication device, a tricky one because it is important to make sure that the person that communicates the taxonomy and the audience for the taxonomy understand each other. So the first thing is to understand - who will be using your taxonomy and how.
As a communication device, taxonomy's principal use is in navigation systems and facilitating good search results. But because a taxonomy maps to a known mental model shared by the user and the system, it is important that the appropriate taxonomy will be exposed to the user in navigation systems, drop-lists, and other actionable interface objects. Such a system allows the user to self-identify: I'm a kid, I'm a teacher or I'm a parent/guardian, and the system renders relevant taxonomies based on appropriate synonym mapping. The multidimensionality of relations within a taxonomic plane is supported by explicit content tagging as well as folksonomy - a taxonomy set by users, to provides the necessary flexibility.