The MEM button has different functions depending on the context.
In idle mode, the MEM button allows browsing for old measurements. More information is available here.
After performing a measurement, the function of the MEM button depends on the Storage Mode.
If Manual storage mode is selected, the MEM button brings up the Save dialog, and allows a measurement name to be typed in.
When any other storing mode is selected, the MEM button functionality is as in Idle mode and allows for browsing for measurements.