The statement about the common weather system-frontal system is correct.

A, the cold front precipitation is mainly behind the front and in the opposite direction to its forward direction, so it does not meet the meaning of the question;

B, cold and warm air meet because the density, temperature, air pressure and other factors are very different, so the area where cold and warm air meet often forms stormy weather, so it is correct;

C, cyclone air flows from all directions to the center, and the center air flow is rising, which does not meet the meaning of the question;

D, the anticyclone center airflow sinks, and it is sunny, which does not meet the meaning of the question.

So choose: B.