Webhooks are a better way for web applications to communicate with each other in realtime. If you provide your users with an API, and they want to listen for new data, they'll do so by "polling"—where they periodically make requests to the API. With webhooks, a user provides a URL, and your application sends new data to their application with a POST request.
You may already integrate with popular services such as GitHub and Slack, but do you integrate with the thousands of other services that your customers may use?
It makes sense to integrate with the services that a majority of your customers use, but there's always a limit; webhooks can help the remaining services (and your customers) integrate with *you*.