SharePoint Taxonomy and Metadata. What is that?

Taxonomy=Categorization
Metadata is data about data. A list of possible metadata values is the simplest form of a controlled vocabulary. The purpose of a controlled vocabulary is to prevent authors from defining meaningless metadata values, from offering too specific or too general metadata values, and to prevent different authors from misspelling and choosing slightly different forms of the same metadata value.
Taxonomy is a collection of controlled vocabulary terms organized into a hierarchical structure. Each term in taxonomy is in one or more parent/child (broader/narrower) relationships to other terms in the taxonomy.

SharePoint Server 2010 supports the following types of controlled vocabularies:

Simple list — this is something that was also available in SharePoint 2007, using a simple lookup list.

Synonyms — It is possible to define synonyms, abbreviations, and preferred terms using the new managed metadata infrastructure in SharePoint 2010.

Taxonomy — Support is provided through the managed metadata infrastructure in SharePoint 2010. In SharePoint Server 2007, taxonomy was implemented through building a hierarchy of sites and subsites that introduced a number of drawbacks. SharePoint 2010 has a built-in hierarchical field control.

Thesaurus and ontology

Folksonomy is a term used to describe the result of adding metadata in the form of open-ended labels called tags by a large group of people. Folksonomy is a form of taxonomy that is built by the end users themselves.