One of new feature in SharePoint 2013 is the ability to drag and drop files into document libraries. This is useful for adding multiple documents to a library and removes the need to open the library in explorer view.
The reason for drag and drop not working and your document library looking like the above screen shot is due to two reasons:
1. You are using Internet Explorer 9 or lower.
2. You don’t have any Office 2013 components installed.
Resolution:
1. This is due to the fact that the drag and drop functionality uses HTML5. Installing Office 2013 will add an ActiveX control to allow you to use this drag and drop functionality in older browsers.
2. If you were to upgrade to IE10 or IE11 the HTML5 would be handled and the drag and drop would be available regardless of whether or not Office 2013 is installed.
Reference link
The reason for drag and drop not working and your document library looking like the above screen shot is due to two reasons:
1. You are using Internet Explorer 9 or lower.
2. You don’t have any Office 2013 components installed.
Resolution:
1. This is due to the fact that the drag and drop functionality uses HTML5. Installing Office 2013 will add an ActiveX control to allow you to use this drag and drop functionality in older browsers.
2. If you were to upgrade to IE10 or IE11 the HTML5 would be handled and the drag and drop would be available regardless of whether or not Office 2013 is installed.
Reference link