Simply stated, this package sync files between servers.
If you change any file like cshtml, script, css etc. and want to push that change on another server(s). File Sync will let you select any number of files/folders and sync them in a flash.
You can also track files or folders for changes and File Sync will let you know what all changed when you last synced. You can them sync changes on a click of a button.
Consider a load balancing scenerio having common database shared among various servers (https://our.umbraco.com/documentation/Getting-Started/Setup/Server-Setup/Load-Balancing/flexible). To sync files you have to depend on some third party file replication service. Instead you can use this package and replicate files among various servers.
You can use this package in conjunction with Umbraco Scheduled Tasks or any task scheduler(like Windows) (https://our.umbraco.com/Documentation/Reference/Config/umbracoSettings/#scheduledtasks). Just set list of files or folders to sync and use POST url in scheduler.