A Closer Examination of the Animation:
Initially, the cold air mass wedges into the warmer air mass ahead of it, (separated from each other by the cold front). The lighter warm air is lifted upwards by the denser cold air and if enough water vapor condenses, clouds develop.

If condensation of water vapor persists, precipitation may develop, typically in a narrow band just ahead of the cold front.

Due to the steep slope of a cold front, vigorous rising motion is often produced, leading to the development of showers and occasionally severe thunderstorms.