A sensitivity case is a specific combination of sensitivity variable values. For example, you specify four values for the average annual wind speed (3 m/s, 4 m/s, 5 m/s, and 6 m/s) and three values for the fuel price ($0.40/L, $0.50/L, and $0.60/L). Then you specify twelve different sensitivity cases because there are twelve different combinations of sensitivity values. HOMER performs a separate optimization for each sensitivity case.
If there are no sensitivity variables, then there is only one sensitivity case.
For more information, see Why Would I Do a Sensitivity Analysis?