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
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. 
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