When you try to add sections by clicking the Home tab, in the Slides group, click on Section, the Add Section command is unavailable (grayed out). The command is also unavailable if you right-click inside of the slides pane in Normal View or right-click inside of Slide Sorter View.
The presentation is in Compatibiliy Mode. The file was saved as PowerPoint 97-2003 Presentation (*.ppt) format. If you look at the Title Bar of the PowerPoint application (bar accross the top of the PowerPoint window) it will read filename [Compatibility Mode] and the file extension is *.ppt.
Convert the presentation to a native PowerPoint 2010 presentation by clicking on the File tab, and in the Info section click the Convert button and save the file as PowerPoint Presentation (*.pptx).
Once you convert the presentation to a PowerPoint Presentation (*.pptx) and open the file in previous versions of PowerPoint you will no longer have the sections visible. However, if you re-open the file in PowerPoint 2010 the sections will be available.
Microsoft PowerPoint 2010, Microsoft PowerPoint 2013, Microsoft Office 2010 Service Pack 1, Microsoft Office Home and Business 2010, Microsoft Office Home and Business 2013, Microsoft Office Home and Student 2010, Microsoft Office Home and Student 2013, Microsoft Office Language Pack 2010, Microsoft Office Multi-Language Pack 2010, Microsoft Office Professional 2010, Microsoft Office Professional 2013, Microsoft Office Professional Academic 2010, Microsoft Office Professional Academic 2013, Microsoft Office Professional Plus 2010, Microsoft Office Professional Plus 2013, Microsoft Office Professional Plus 2010 Home Use Program, Microsoft Office Standard 2010, Microsoft Office Standard 2013, Microsoft Office Starter 2010