I do not understand how you can earn the Tag-Editor badge. What do you have to do and where?
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When you click on a tag (such as the ones visible under this very question ("support", "badges", and "tag-editor")), you will see a short exert from the tag's "Tag Wiki", which is a short description of what that tag is for and how it relates to StackOverflow.
Beneath that exert is a link titled "improve tag wiki". It is on this page that you'll be able to improve the description of a tag in order to earn this badge.