Overcast skies are like a big softbox...giving you very soft, even light. This can be great compared to sunny skies, which give you very bright highlights and dark shadows.
For example, if you are shooting a portrait outdoors, you probably don't want to have your subject in bright overhead sun because the highlights and the shadows will be vastly different.
Same deal with landscapes etc.
In overcast weather, the highlights won't be as bright and the shadows won't be as dark...thus compressing the range of the scene, maybe bringing it within the dynamic range of your camera, allowing you to get the shot without blown highlights or lost shadows.
Of course, overcast skies typically don't look good when they sneak into your image.