A 'Webhook' is a user defined callback that can be registered on a website in case you want to react to certain events.
For example something that is often done is responding to events in a gtihub repository, like when someone does a check-in or an issue is added. Typically you would want to trigger a build when a check-in happens. You can register a callback/webhook on github which points to a url provided by you that reacts to the HTTP POST called by github.
Azure function can be configured to be triggered by a normal HTTP request or it can be setup as a webhook i.e. it will be called whenever a specific event on some website has occurred. Functions configured as webhooks will respond only to a HTTP POST. There are already built in values to set up an Azure Function as a github or Slack webhook.
If you are not reacting to an external event or cannot register a webhook in the event source just go with the HttpTrigger and explicitly invoke your function.