Web hook is a way to send data over the internet. The data can be anything, a sales order, an advanced shipping notice, employee onboarding data etc. Once you have this information, you can do anything you want. With ERP systems in the cloud, this technology is perfect for use to integrate systems in ways not previously possible for SMB's.
Setting up a web hook requires native support from your application, or at a minimum the ability to interface with your application. I prefer the later, It allows for more flexibility. Rarely are you going to find that your business partner (customer or vendor) has the exact format that your system needs. Through any of the cloud providers you can easily setup a service to receive the Information (web hook), translate it if required and consume it in your application. This method achieves a highly scalable, fault tolerant solution and also provides a way for self-hosted systems to benefit from the integration.
Web hooks avoid all the pitfalls of the old EDI standards. The old EDI standard was difficult to maintain and impractical for SMB's in my opinion. With web hooks, data is sent as JSON payload and with the plethora of tools available to extract the JSON data, integrating the information into your business process becomes (almost) trivial. Setting up an endpoint that sits waiting to receive a web hook is simply a matter to taking you preferred web development tool and creating a web page that receives a http POST method. Once that's done, upload it to one of the cloud providers so you don't have to host it your self and you're all set.