The rule of thirds might be one of the main actors. But when the supporting actors do their job badly, the main actor cannot save the day neither. On this account it is enormously important to choose the proper sky when you make pictures (provided it is necessary to show some sky). Therefore try to avoid pale or even grey colored sky into your photos.
In other cases the general rule is: shoot preferred pictures with the sky, when the sky has an attractive color. Whereby it does not necessarily have to be always blue. For example early in the morning, it has wonderful red or orange colors and creates a great atmospheric mood.
In case you see some clouds, it would be even better. Because clouds appear in all kinds of shapes and forms, they emphasize the whole composition additionally. Note that the sky should also be placed by using the rule of thirds. Otherwise, your picture could lose the tension.
But again, take the rule of thirds not as a strict order but just like a recommendation. For sometimes you can break this rule.
I hope, I could give you some useful information about the meaning of the sky in photography which belongs to the photography basics. Regard the information in this article as a first step on your way to learn photography seriously. To act like a pro, you need to inform yourselves more into depth. For this reason I can recommend you this book: BetterPhoto Basics* from Jim Miotke. Here you will learn all the photography basics a beginner should know to become a good photographer.
*Affiliate link: if you click on the link, no costs will arise for you. If you decide to make a purchase, the product will keep the same price. But I will receive a small benefit from this supplier, which I would reinvest to keep this blog alive.