The CAPTCHA is a puzzle to solve to show that the user is a real person rather than a bot. The MEpedia CAPTCHA puzzle appears when a user creates a new page or makes an edit that adds an external link (whether in the form of an inline reference or otherwise.) This requirement helps prevent ref spam.
Some commonly used, reliable sources are on a whitelist so that users may add references to them without having to solve the CAPTCHA. (It should be as easy as possible to add high-quality references!) If you have a source to suggest for addition to the whitelist, please add the URL here: MediaWiki_talk:Captcha-addurl-whitelist#Proposed_websites_for_white_list. An administrator will review the suggestion and add it as appropriate. (To prevent vandalism, only users with administrator and/or bureaucrat permissions are able to edit the whitelist.)