A Webmention is a way to notify websites when a link to a website is posted on a different website.
The purest form of this is where a website owner hosts a webmention endpoint that can receive webmentions, store them in a database, then display them on the appropriate page. Running this server is generally a little more involved but luckily there is a handy service called webmention.io which handles the receiving, storage, and provides a REST endpoint for fetching webmentions.