Web Hooks or Webhooks are a relatively modern invention. They are essentially an API designed to send information in real time.
For the non-technical, who know that integration is an important aspect of a product's capability and a good demonstration of its maturity, we recommend you get your development team to peruse out RESTful API documentation and to share their opinion on just how comprehensive it is.
Gemini is a transactional system, in effect task management. A Gemini webhook therefore provides a callback with real-time information on a newly created or updated task. So, if a task is a ticket, or a bug, or a change request, every time one is created or modified your external application can get hold of all its details and do whatever it is you want to do with that information.
There's not a lot more to say, except that it's a minute's work to configure Gemini webhooks and webhooks themselves are just a part of Gemini's App Framework, under the sub-heading of Event Apps.