Think of it as a chess match: the storm versus local weather patterns. The cone represents an analysis of all possible moves that can be made, with suppositions on the most likely ones that will be made given all known conditions. That's why it gets more accurate the closer to the present date.
And it shows _the center of the storm_ not the size of it! The cone is designed to be statistically correct 2/3 of the times, too, so bottom line: you are _not_ out of trouble of you are not in the cone!
As always listen to your local NWS forecast: they stack regional high precision models and meteorologists analysis. Best of both worlds: the brilliant brains and the supercomputer going full throttle!