Official Response and explanation from Microsoft: Outlook 2013 Folder Pane Disappears After Installing September 2013 Public Update
If you lost your navigation pane after installing the September patches, you'll get it back after you install the August 13 2013 hotfix.
Read about the hotfix at Description of the Outlook 2013 hotfix package (Outlook-x-none.msp): August 13, 2013
Request the hotfix without reading about it: Hotfix Request
Uninstalling Update for Microsoft Office 2013 (KB2817630) will work too, but the hotfix fixes quite a few problems too.