A gust front is the leading edge of the downdraft from a thunderstorm.
This is where cool air rushes down and out of a thunderstorm.
There are two main reasons why the air flows out of some thunderstorms so rapidly.
The primary reason is the presence of relatively dry (low humidity) air in the lower atmosphere.
This dry air causes some of the rain falling through it to evaporate, which cools the air.
Since cool air sinks (just as warm air rises), this causes a down-rush of air that spreads out at the ground.
The edge of this rapidly spreading cool pool of air is the gust front.
The second reason is that the falling precipitation produces a drag on the air, forcing it downward.
The front is usually marked by gusty cool winds, and sometimes blowing dust.
You will feel the wind from the gust front before it starts to rain.
If the wind following the gust front is intense and damaging, the windstorm is known as a downburst.