A webhook URL can also be referred to as "web callback" or an "HTTP push API". These may be the definitions you have previously seen.
A webhook operates on the concept of "event reaction" (e.g. Don't call me, I'll call you if I have something new). In other words, this means that there is no need for constant polling of the server-side application by the client-side application. Instead of the client-side application constantly polling the server-side application to check for new events, the server-side will call the client-side (e.g. I have something new for you now) when the server-side has something new to report to the client-side.
This is done by invoking a client-provided webhook URL.