السماء الدنيا "the nearest sky" is the sky nearest to Earth according to the majority of commentators. This can either mean a few things:
It is the sky nearest to us(atmosphere or upper atmosphere/sphere of the moon, by which we see the light of the stars/planets upon it's blue surface at night. )According to Razi and other commentators, it need not be that the Stars are actually located in the nearest sky السماء الدنيا, but rather they can be located in a sky above it. This is because space is transparent and if they are in the highest skies or in the nearest, you still see their light appearing in the nearest sky. Imam Ibn Ashur in his tafsir compares this idea to saying the moonlight beautified the lake, the moon isn't in the lake but it's light beautifies it and reflects from it's surface. Likewise, when the Qur'an says:
"Indeed, We have adorned the lowest heaven with the stars for decoration" (Surah Saffat verse 6)
The Stars beautifying of the nearest heaven need not necessitate they are in the lowest sky. Scientists today know that our perception of the stars and celestial objects are all affected by atmospheric refraction. They compare it to seeing something at the bottom of a swimming pool. Thus, if one sees the sun at the horizon, one might be seeing it before it has actually risen in actuality due to refraction, or if at sunset, one may still see it, even after it has set.
Another interpretation is that the Nearest Sky is our Milky Way galaxy, since the majority of stars seen at night are in the Milky Way.
The most common interpretation is that the Nearest sky is our entire universe of stars/galaxies etc.
Tafsir Qurtubi mentioned similar interpretations at his time. Some said that the stars only give light in the nearest heaven, others said the stars give light in all the seven heavens.
For more information you can see my book "Mysteries of the Qur'an: Seven Heavens" available on Amazon, under my pen name Israfil Sulayman.
سماء In the context of the Qur'an سماء is sky. In Classical Arabic sky is anything that is above. So If I am above someone else looking at them below, one could say that I am " سماء" in relation to that person. In Old Arab usage, it could be used to mean "Roof", as the Arabs would sometimes refer to the roof of a house as the سماء al bayt" lit. "The sky of the house." but in actually they were referring to the roof. سماء is what's up, what's above. That's it's linguistic significance.
سماوات is plural of سماء