Hurricane and tropical storm watches and warnings are based on the potential intersection of the storm's hurricane-force (64 kt) or tropical storm-force (34 kt) wind fields with a land mass within - realistically speaking - a time frame of 24 to 48 hours. Based in the track, intensity, and size forecasts, their associated uncertainties, and climatological modeling, the graphical wind speed probabilities product is a relatively new effort on the part of hurricane forecasters to portray the problem to the public visually. Probabilities that a given wind speed (hurricane-force or tropical storm-force) will intersect specific locations as the result of a storm in the vicinity are issued for all the standard forecast periods through to 120h (five days). The graphical probabilities, like this one, cover the total accumulated probabilities (cumulative probability) that the designated wind speed thresholds will be surpassed at specific locations through to the end of each forecast period.

This example is for Hurricane Dean of 2007, one of the most intense hurricanes to ever make its way through the Atlantic basin. Dean intensified to a high Category-5 storm (165 mph winds, central pressure 906 mb) just as it was getting ready to make its first landfall on Mexico's Yucatan peninsula.
The Hurricane-Force Wind Speed Probabilities product (above) described the probability at that time that hurricane-force winds from Dean would occur at specific coordinates of latitude and longitude sometime within the 5-day (120h) forecast period. Whether or not that would actually happen at any given place would, of course, depend on the track that the center of Dean would ultimately follow, as well as on the radius of the 74 mph or greater winds in the relevant quadrant of the storm.
It is of note that even though Dean was a Category-5 hurricane, the Hurricane-Force Wind Speed Probabilities product will look the same whether the expected winds expected are just above 74 mph (Category-1 force) or 155 mph (Category-5 force). From Dean, it was the central part of the peninsula facing the Gulf of Mexico that received the Category-5 (150 kt = 173 mph) winds.
As the westernmost portion of the 70-80 percent probability zone was touching the edge of the eastern Yucatan peninsula, there was believed to be a 70-80 percent probability that that segment of coastline would experience hurricane conditions (sustained winds at 74 mph or greater) at some time during the 5-day (120h) forecast period. Because of the forecasted speed and direction (track) of the storm, as well as the size and structure of its wind field, this was expected to happen within the subsequent 24 hours. Hence, that area was placed under hurricane warnings, marked out in red in the 5-day cone (below).

The stretch of the coastline to the north of the hurricane-warned areas, and the bend area, to their west, were not under hurricane warnings but tropical storm warnings and watches (blue and yellow regions in the above cone), respectively.
The five-day Tropical Storm Force Wind Speed Probabilities (below) issued with the advisory indicated a reasonable chance that those areas - though they might be spared Dean's hurricane-force winds - would still get its tropical storm-force winds.

What Dean actually did is below. It crossed over the Yucatan peninsula at maximum intensity along a track very close to what was predicted, with the northern part of the peninsula to its right, the southward bend area to its left, and the small town of Mahajual, Mexico, through its center.
