The Quick Reply box appears underneath topics enabling a member to post a message on the same topic page, rather than clicking the reply button and loading a new page to post a reply on the posting screen.
Quick reply can be disabled, enabled, and enabled but collapsed by default for any members by applying their preference for it in their [[Profile (term)|profile].
Administrators can also set the default display of quick replies by a per-theme basis (Admin > Themes and Layout > Reset Options).