Why do people use "skies" instead of "sky" (when, indeed, we only have one sky)?
Reach for the sky/skies!
I'm glad to finally see some blue skies.
I'm glad to finally see a blue sky.
Skies is a poetic/literary word used to mean heaven or "heavenly power." The first example sentence could mean "reach for heaven."
In some set phrases, the used word is skies, as in "he wrote to his sister praising Lizzie to the skies," where "to the skies" means very highly or enthusiastically.
According to the OED, the earliest meaning of "sky" in English was "cloud" (which is what "sky" still means in Scandinavian languages).
From that "the skies", originally meaning "the clouds", came to mean "heaven", or "sky" (in the modern sense).
The OED lists "sky" in the modern sense as the third meaning. It doesn't spell it out, but I think that what happened is that once "the skies" took on the meaning of "the expanse of heaven", it was no longer felt to be plural, so people started referring to it as "the sky". If this is correct, then "the skies" is simply an older form, which survives in poetic use and a few phrases.
I've never heard "reach for the skies", only "...sky".
"I'm glad to see some blue skies" implies multiple instances, e.g. a few days in a row with blue skies. (It's usually black in between. :-) ) "...a blue sky" means one sighting.
The other place where I've heard "skies" is with respect to airlines ("fly the friendly skies" is some airline's slogan). I think this is by analogy with "seas" and ships.