Use the adjective overcast when you're describing a cloudy sky. An overcast day can be dark, cold, and gloomy, or just quiet and calm.
A day that's gray and cloudy is overcast, and a dull, sunless sky can also be described this way. A less common way to use overcast is when you talk about sewing — an overcast stitch catches the edge of the fabric to keep it from fraying — and the stitch itself is sometimes called an overcast. Before the weather-related adjective was coined, overcast was a verb meaning "to cover" or "to overthrow."