Interface administrators are the only users with the ability to edit sitewide CSS and JS pages (such as MediaWiki:Common.js, MediaWiki:Vector.css, interface messages which are interpreted as raw HTML, or the gadget pages listed on Special:Gadgets), and other users' personal CSS/JS pages. JS and CSS pages are executed by the browser of wiki editors and readers as code, which can be used to change how content is styled, change the behavior of pages or even create highly complex tools.
Editing CSS/JS that gets executed in other users' browsers is very powerful and potentially dangerous in the hands of a malicious user. Interface administrators should be users who need it, who are trusted by the community, and who follow common basic password and computer security practices (use strong passwords, do not reuse passwords, use two-factor authentication, do not install software of questionable origin on your machine, use antivirus software if that's a standard thing in your environment).
Administrators and interface administrators can edit pages that are not CSS nor JS in the MediaWiki namespace. (e.g. MediaWiki:Sidebar)
Apply to become an Interface administrator
To apply for interface administrator access, apply at Wikiquote:Requests for interface adminship.