Taxonomy is formally defined as the practice of classification according to natural relationships.
The taxonomy can be thought of as a system of classification or a hierarchy of terms that includes synonyms, translations and descriptions
A very good example, to understand the basic concept of taxonomy and its need, is looking at biological classification Kingdom-> Phylum-> Class-> Order-> Genus-> Species we learned in high school biology.
In SharePoint 2010, Taxonomy Support is provided through the managed metadata infrastructure.
Managed metadata is a hierarchical collection of centrally managed terms that you can define, and then use as attributes for items in SharePoint 2010.