A folksonomy is a classification system on the basis of user-generated tags.
“In a folksonomy, the relationships between tags are inferred based on their usage patterns. There are no formal relationships in a folksonomy, other than perhaps ‘degree of relatedness’. Because a folksonomy uses agorithms to look at tagging patterns, two tags that have no known semantic relationship may have a statistical relationship.”
Gene Smith, Tagging: People-Powered Metadata For The Social Web, p. 82