GFS:

The Global Forecast System (GFS) is a global numerical weather prediction computer model run by NOAA. This mathematical model is run four times a day and produces forecasts up to 16 days in advance, but with decreasing spatial and temporal resolution over time it is widely accepted that beyond 7 days the forecast is very general and not very accurate.

The resolution of the model horizontally, it divides the surface of the earth into 20 kilometre grid squares; vertically, it divides the atmosphere into 64 layers and temporally, it produces a forecast for every 3rd hour for the first 240 hours, after that they are produced for every 12th hour.

NWP:

Numerical weather prediction uses current weather conditions as input into mathematical models of the atmosphere to predict the weather. Although the first efforts to accomplish this were done in the 1920s, it wasn't until the advent of the computer and computer simulation that it was feasible to do in real-time. Manipulating the huge datasets and performing the complex calculations necessary to do this on a resolution fine enough to make the results useful requires the use of some of the most powerful supercomputers in the world. A number of forecast models, both global and regional in scale, are run to help create forecasts for nations worldwide. Use of model ensemble forecasts helps to define the forecast uncertainty and extend weather forecasting farther into the future than would otherwise be possible.

Wikipedia, Numerical weather prediction, http://zh.wikipedia.org/wiki/數值天氣預報(as of Feb. 9, 2010, 20:50 UTC).