I'm not sure what the number itself means other than the hotest NGK is a '2' and the coolest NGK is a '13'.
As I understand it (and there are probably people on the list who know more about this than I), the heat rating refers to how hot the ignition end of the spark plug stays basically due to the thermal mass and surface area of the plug that's actually exposed to the combustion chamber.
A hot type would be used in a lower RPM engine so it would retain heat between combustion strokes. When a plug is too hot for a specific engine, it can cause pre-ignition.
A cooler plug would be used in a higher rpm engine to help prevent pre-ignition, but a plug that's too cold would tend to foul quickly.
I've only played with heat ratings of plugs on two stroke dirt bikes. I've gone to a step cooler plugs after going to hi-comp pistons and tuned a carb to run on the lean side for the best power. Sometimes even with high octane pump gas or 100 octane race gas I've had detonation issues and a cooler plug will help aleviate that. I've also run a hotter plug to prevent fouling when I've gone up significantly in elevation (bike running richer) and didn't want to re-jet the carb.
I'd assume that something similar would be true with a 4-stroke twin, but the margin for error would be greater since there is twice as much time between combustion strokes, which is why someone can run a DPR9 and I can run a DP8 (both mostly stock engines) and both of our bikes run fine.