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The Cone
Forecasters create the cone of probability by drawing a series of ever-larger circles along the predicted path of the hurricane. The size of each circle takes into account the historical error in hurricane prediction going back five years, and each is meant to represent a two-thirds probability that the eye of the hurricane will fall somewhere in that circle as time goes on. The three-day forecast is typically much more accurate than days four and five, and the National Weather Service colors the three-day cone white to highlight this more accurate prediction of the storm's behavior.
Computer Models
The predictions used to draw these circles come from computer models. Many different organizations attempt to forecast the weather using complex computer programs that take into account many different variables and conditions, and then compute a prediction based on this information. Typically, predictions of storm behavior in the immediate future are usually accurate, because the number of variables and uncertainties is low. As the predictions move further into the future, however, more variables and potential changes to the conditions creep into the forecast, reducing its accuracy. For this reason, a plot of these forecast storm paths from many different sources may seem relatively coherent for the first few days, only for the predictions to diverge widely as time goes on.
Regular Updates
Since weather forecasting is much more accurate in the short term, when a dangerous storm threatens human life, the National Weather Service regularly updates their cone of probability as the hurricane nears landfall. When a storm is still out at sea, updates may come once a day, but as it nears populated areas, they may produce new predictions several times a day in order to provide the best possible forecast for those who might be in the storm's path. Since weather is naturally difficult to predict, the events of a few hours, as well as updated information from sensor buoys or flyovers, could drastically change the predicted path of the storm.
The Cone and the Eye
If you find yourself in a region threatened by a hurricane, you should keep in mind that the cone of probability only estimates where the eye of the storm might be at any given time. Hurricanes can stretch for hundreds of miles, and they can affect weather patterns well outside the storm's central rotation. If the cone of probability suggests the storm may come anywhere near where you live, you should plan accordingly.