Files stored in a Document library can also be edited in a client application using WebDAV directly on the live site. There is the Edit action available in their drop-down menu, as can be seen in the screenshot below. Clicking the icon opens the document for editing in a client application (if there is an application for the particular file type installed on the client machine and if the application supports WebDAV).
For this action to be enabled, the document must have one of the supported extensions (see Settings for more details) and the Modify permission for the particular document must be granted to the current user. Please refer to Modules -> Document library -> Security for more details on permissions in document libraries.