RAP:

The Rapid Refresh (RAP) is a NOAA/NCEP operational weather prediction system comprised primarily of a numerical forecast model and analysis/assimilation system to initialize that model. It is run with a horizontal resolution of 13 km and 50 vertical layers. ,
The RAP was developed to serve users needing frequently updated short-range weather forecasts, including those in the US aviation community and US severe weather forecasting community. The model is run for every hour of day and is integrated to 18 hours for each cycle. The RAP uses the ARW core of the WRF model and the Gridpoint Statistical Interpolation (GSI) analysis - the analysis is aided with the assimilation of cloud and hydrometeor data to provide more skill in short-range cloud and precipitation forecasts.

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).