Forecasting Models are just what they sound like-mathematical models run on computers to simulate the future conditions of the atmosphere.Today's state of the art models are very complex,but I'll attempt to give an accurate but brief overview.A model is a computer program the recieves input from an automated system of observations at the surface and high up in the atmosphere.Once it is given the input,it begins to simulate what will occur over a given period of time by solving known atmospheric physics equations with the observations put in.Models inherently become less accurate the longer away the forecast is for;in other words,a forecast for 10 days is much less accurate than one for tomorrow.
There are several types of forecast models.Firstly,the most basic and oldest are the statistical models.These programs are full of historical data:they know what has happened in the past.So,when told what is going on right now,they look at similar events from the past,find the best matches,and make their forecasts based on that.These models are typically available the soonest,but are often the least accurate,expecially when unusual weather patterns are in place.
Next there are the dynamical models.These typically have no knowledge of past events and rely entirely on physics to make their forecasts.These are often the most accurate models,and take the longest to be available.
The cross-breed between them are the statistical-dynamical models,which rely on both past events and physics to make their predictions.They are often more accurate than the statistical models.
Here you can find all of the hurricane forecast models on one map.Please remember,XTRAP is not an actual model.Also,not all of the models are of equal skill.
Here are the NWS's suite of models.Generally,different models are better in different situations.The RUC works best for the next several hours,the NAM works best in the 1-4 day range,and the GFS is the best when it comes to tropical cyclones and long range predictions.
Here is FSU's Tropical Model Page.This is probably the best for hurricane forecasting.