"Probability" is the term used to describe the likelihood of something occurring. In this case, it is the likelihood of temperature dropping to freezing or below freezing - a "freeze event". Mathematically this is quantified through the ratio of the number of historic freeze events that have occurred on, before, or after a specified date to the total number of all scenarios (in this case freeze and non-freeze events) that have occurred on, before, or after the same date. If a probability is low, it means an event is not as likely to happen. If the probability is high, the event is more likely to happen.

For the shading on the map, an Inverse Distance Weighted interpolation method is used. Parameters include a power setting of 4 and a search radius that is variable with a number of 6 points. The resulting raster has a cell size of approximately 0.05 decimal degrees. It is then clipped to the Continental US before displaying on the web map application.

More information on Inverse Distance Weighted interpolation can be found on ESRI's Tool Reference webpage for IDW:
https://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/idw.htm