As a cold front moves into an area, it displaces warmer air at ground level. Colder air is denser than warm air, so it pushes the warm air higher into the atmosphere. Temperature changes along the boundary of the cold/warm air can be in excess of 50° F.
If enough moisture is present, a narrow line of thunderstorms and rain can form along the edge of the cold front. If the cold front boundary is unstable, thunderstorms are more likely. Stable systems often just bring steady rains. Very unstable cold fronts can generate hail storms and even tornadoes.
Cold fronts usually move from northwest to southeast. They tend to be strongest in the spring and the fall and weakest in the summer. In addition to rain and thunderstorms, they also bring gusty, shifting winds.
Cold fronts move much faster than warm fronts and can cause sharper changes in the weather. As a cold front is passing through, you will notice temperatures drop quickly and then steadily decline as it passes.
If you're watching the weather forecast on your local news, a cold front will be marked by a solid blue line. The blue line marking the cold front might also include triangles pointing in the direction the cold front is moving.