The Move command is only available to logged-in users; it changes the name (and sometimes the namespace) of a page, leaving a redirect behind and preserving the entire page history at the new location.
Exceptions and problems
Pages cannot be moved on top of existing pages by non-sysops, unless the target page is a simple redirect to the page being moved there (for instance, if you moved Mafioso to Mafiso accidentally, you could move the page back without any trouble. But you could not overwrite Townie with Mafioso, because that page has a history. If you need help with a blocked move, contact a sysop.
Overuse of this command in sequence can cause problems; the MediaWiki software only follows redirects once, to avoid infinite looping. Adam Weishaupt is a good example of this phenomenon; other problems can be found at Special:doubleredirects.