More specifically, what role do humans play in digesting the output of the computer model and producing the forecast? What adjustments or corrections are made to what the model says is going to happen, and based on what reasoning? "My gut tells me the tornado is going to move east, even though the computer says it will move west with an estimated 98% likelihood"?
Are the humans doing more than creating a human-consumable verbal summary of what the computer model says will happen -- explaining the severity and location of the predicted weather in human terms?
At each National Weather Service office, forecasters typically use model output to guide their daily forecast products, such as temperatures and precipitation probabilities. However, these forecasters are aware of smaller-scale nuances of their forecast area, such as topographic influences, land-sea interactions or urban heat island effects, which models may struggle to resolve. Human knowledge of model limitations helps to produce a better forecast.
A further example would be hurricane forecasting, where National Hurricane Center forecasts typically outperform most models (see http://www.nhc.noaa.gov/verification/verify6.shtml for starters).