One of the most useful features of SharePoint 2013 is the ability to drag and drop documents or entire directories into Document lists.
The drag and drop feature requires an IE version 10 or greater OR Office 2013. Our current standards for our users were IE9 and Office 2010, so of course they weren’t seeing it. I’m running IE10 and have both Office 2010 and Office 2013 installed for development purposes, which satisfies the requirements for it’s use. Importantly, this doesn’t mean that it’s impossible for users with IE9 or lower or Office 2010 to use it.
The simple solution is to install SharePoint Designer 2013 and choose Custom Installation. Deselect everything (including SharePoint Designer) except Office Tools. This will install the correct Active-X control and allow the drag and drop functionality to work.