The Sync Function in Sync Gateway is a crucial component that determines which user has access to specific documents. To synchronize documents with users who haven't logged into the app yet, developers can use the public channel, also known as the ! channel, to insert a "Getting Started" note automatically when the user starts the app for the first time. This feature allows for dynamic data changes on the backend and is particularly useful in applications like note-taking apps. The Sync Function involves mapping notes created by registered users to channels accessible only by that user, enforcing write permissions with the requireUser method, and testing it using curl commands. By leveraging this feature, developers can create a seamless onboarding journey for their users.