Fastly caches objects for a certain period of time up to their TTL. After that the object will not be requested from the web server or Magento again. Until the TTL expires Fastly will deliver the cached object no matter what will change within Magento or the webserver's file system. To force Fastly to cleanup its cache and to retrieve the information again from the backend you can trigger a purge request right from Magento.
In the Magento2 backend go to System -> Cache Management. If you have enabled the Fastly_Cdn module in the configuration you will see three new buttons "Additional Cache Management" section.
You can purge objects in Fastly's Cache based on its content type by just clicking "Clean Fastly CDN Cache by content type". This will allow you for example to remove the CSS files of all store views in Fastly if they have been modified without the need to invalidate any other object which will save a lot of resources on high frequented stores.
You can purge objects in Fastly's Cache based on the store by just clicking "Clean Fastly CDN Cache by store". This will only remove content that is generated from Magento. Images, CSS files or JavaScripts will not be purged.
It is also possible to purge a single URL (e.g. page) using "Quick Purge". Enter the desired URL in input field next to "Quick Purge" button and press it. If URL is valid you'll see a success message for purged page.
Beside these direct purge requests Fastly_Cdn has observers for "Flush Magento Cache" and "Flush Cache Storage" to purge all objects in Fastly together with the Magento cache refresh. It also has observers for "Flush Catalog Images Cache" and "Flush JavaScript/CSS Cache" to clean objects that match the appropriate surrogate keys in Fastly. All HTML objects will be purged too as the product image and JavaScript/CSS paths will change when Magento generated them again so the cached HTML objects might contain wrong paths if not refreshed. You can also enable automatic purging of CMS pages, categories and products when they are saved (see configuration). If you don't want these observers to take automatic action comment them out in the config.xml of the Fastly_Cdn module.