For example, if I’ve built a full conversational flow in a service like API. AI that results in a booking being made. How do I actually then make that booking sync to a third party calendar?
Can this be done directly between the two? Would I need to build an application to sit between the two?
I’m tech inexperienced, so I’m curious how these things work…
You will need to add "fulfillment" to your API.AI app, and yes, have a custom application (the "webhook") in between.
That is, once you've collected all the information to make that booking, you don't want to just say "Thank you, here's the book information you've provided [...]", you want to do things with it. That's what fulfillment does. API.AI will send a REST call to your webhook with the information the intent has, you do whatever you want with it (e.g.: actually add the booking to the calendar), and also return the response that you want API.AI to give, that'll take the place of the "text response" you normally provide for a given intent.
To set this up on the API.AI side, there are two steps: Find "fulfillment" in the menu for your app, and tell it how to connect to your webhook. Then go to any intent where you want the webhook to be called when it's matched, and select "use webhook" under "fulfillment".
The more involved part may be to actually provide a webhook that API.AI can call - that's where your custom logic goes, it sits between, in your example, the API.AI app and the calendar application and makes things actually happen.
Useful reading: https://docs.api.ai/docs/webhook