Exporting a CSV of taxonomy terms
If you want to export taxonomy terms specifically to import them into another Drupal site, you should use Taxonomy Manager (if you need it for other pieces of its functionality) or Taxonomy CSV import/export (tutorial here). If you want to just export the data stored in a taxonomy as a CSV file (e.g. for archiving), using the Views Data Export module is an option.
Make sure you have Views Data Export installed and enabled, and create a new view. For this view, instead of showing "Content", use the drop-down to select "Taxonomy terms", then the vocabulary you want under "Type". Create a page, choosing "Unformatted list" of "Fields", and hit "Continue & edit".
By default, the only field that appears there is "Taxonomy term: Name". You can also add "Taxonomy term: Term description" to get the value of that field, or add any other custom fields you've added.
To get information about the parent term, toggle open the "Advanced" section of Views and add a relationship "Taxonomy term: Parent term". Then you can add another field for "Taxonomy term: Name", and when you configure it, you can select "Parent" under "Relationship".
Add a "Data export" display, give it a path, and attach it to the page you created, if you'd like. The rest of the configuration for Views Data Export is the same as described in section 15.2.