Taxonomy refers to the organization of content around keywords that describe the content. Unlike heirarchical menus, Taxonomies don't have a "one-to-one" requirement that each page have exactly one taxonomy term. Taxonomies can span different types of content as well; for example, users can click on a taxonomy link at the bottom of an FAQ and see a list of Announcements and Press Releases that share the same topic.
"Pre-defined" taxonomy means that site administrators define a vocabulary of words in advance, and when editors create or edit content, they can choose from among those terms.
"User-defined" taxonomy refers to vocabularies that can be added to on the fly by editors as they create or edit pages.