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A webhook is a mechanism for notifying a server about updates to some content in realtime by making an HTTP request. Often also referred to as a "callback URL".
Often the payload of a webhook is something small, such as a message that indicates new content for the application or for a specific user, rather than including the actual data itself.
APIs that support webhooks
Instagram has a realtime API which sends updates to your application any time any authorized user posts a new photo.
Apps can register webhooks with the Jawbone API to receive callbacks for user events.
It is possible to register a webhook in the Beeminder API so that the API will notify the webhook when any of your goals have new data. This was demoed at the 2012 IndieWebCamp.
Known supports sending notifications to an arbitrary webhook via a plugin: https://github.com/idno/Webhooks
GitHub has extensive webhook support. Most activities related to a repository can send a notification through a webhook. One can even trigger when a pushed commit for a GitHub Pages has been published, which is useful to trigger PubSubHubbub pings. 
Reading.am supports webhooks for saved pages
Examples of IndieWeb sites that have enabled some form of webhook:
- phorkie sends notifications via webhooks when pastes are added, updated or deleted. See the documentation.
- Chris Aldrich uses the webhook functionality of IFTTT to syndicate (via PESOS) data from a variety of silos to his website using Micropub. He's described the set up in more detail on 2020-01-21 in Using IFTTT to syndicate (PESOS) content from social services to WordPress using Micropub
- Silos include: Goodreads, GitHub, Hypothes.is, Last.fm, Spotify, Untappd, Twitter, Letterboxd, Diigo, Reading.am, Huffduffer, Google Calendar, Meetup.com, YouTube and Pocket.