Core plugins in WordPress are community-developed plugins that are tested and developed alongside the WordPress core codebase. They aim to remove single points of failure, promote good practices, provide niche features on a separate cycle from core, remove bloat from the core code, and make it easier for developers to get involved. Some examples of core plugins include Importers, Health Check, and Post-by-Email. Developers can get involved with core plugins by contributing on their Trac projects or mailing lists.