Did you configure the button with which the OSD is turned on/off?
In MSI Afterburner>Settings>On-Screen Display>Toggle OSD. Set a key for it, and try using it.
If it still doesn't work,
Settings>Monitoring>Framerate(in the list of items shown)>Check 'Show in OSD'
If you've already done the above steps, the 'Properties' column in the Monitoring tab should show 'in OSD' in the Framerate section.