During a very heavy rainstorm, the downward force of the falling rain creates a cool, strong, sinking wind. As this rush of air reaches the ground, it races outward ahead of the storm.
Thus, someone standing ahead of the storm will get a rush of cold air preceding the thunderstorm. That's known as a gust front. Some of the strongest storms can create gust fronts with wind speeds over 80-100 mph.
Gust fronts can also spawn a secondary storm near the original thunderstorm. As the cold air rushes outward, it can force the warm air on the ground to rise up and condense, leading to additional thunderstorm development.