Vue.js is a JavaScript framework that is used in the MediaWiki project (and just about everywhere else) for creating the frontend. For MediaWiki, Vue.js in used in the new Codex design system for Wikimedia. Codex replaces MediaWiki UI (and OOUI) which relied heavily on jQuery. While jQuery was great - and is still shipped[1] with MediaWiki core, the JavaScript and browser landscape has changed significantly leading to whole new JavaScript libraries and frameworks such as Vue.js.
https://gitlab.wikimedia.org/repos/design-systems/CodexExample is a repo that shows how to leverage Codex in your MediaWiki extensions.