As the winds circulate around a frontal depression, they bring warm air into an area of cold air and vice versa. This makes warm and cold fronts. A cold front is where cool air pushes under the warm air, forcing it to rise. Where warm air advances into an area to replace cold air, it is known as a warm front. And the warm air rides up over the cooler air.
Clouds form along a cold front as the air rises.
Because they form along the front, the line they make is often very clearly defined. And because the air is forcing itself underneath the warm air, it kind of curves as it goes upwards. This means the layer of clouds pushes forward the further up you go. I've tried to do a diagram below. With a warm front the opposite happens.