When you have overcast skies the whole sky becomes your light source. Therefore when you include the sky in your composition you are effectively shooting into your own lighting. This makes it very difficult to expose for the light source itself and the subject and the rest of the scene.
When you have a sunny day the sun is your light source and the rest of the (blue) sky is just another part of the scenery, which makes it relatively easy to photograph, unless you include the sun itself in the frame.
In the situation of overcast skies I will shoot raw and manually set an exposure that puts the brightest part of the sky at the brink of clipping. Then using software I will adjust the rest of the scene until I get an aesthetically pleasing/acceptable result. Here is one such example....
The red areas show the clipped highlights. The blue areas indicate clipped shadows. You will see that I have been able (quite easily) to lift the details in the shadow areas and mid tones without losing anything in the highlights. The tiny area which remains clipped is, IMHO, inconsequential and I've retained plenty of detail in the sky.
Another example here, this time without the need to lift the foreground, but still shot with a manual exposure to secure enough of the highlights from the backlit sky to be able to manufacture a usable image. Once again the exposure was locked manually based on metering the sky, not the subject, and checking the histogram and highlight alert blinkies....
Others have suggested alternative approaches, which might give you a better result in the end, but aren't always viable when the scene includes movement or may require a bit more setting up before the shot.