Aside from astronomical/environmental considerations, what is the signifcance of what you see when you look at the sky? Why?

This time of year? Weather or not its going to thunderstorm so i can or cannot take my afternoon swim at the YMCA. ;)

If you were an amateur astronomer you wouldn't have to ask.

Assuming you mean the stars and planets, I'd say their significance is in illustrating the sheer scale of the Universe and our very insignificant part in it. With the naked eye, we can see only our fellow-planets and part of our own galaxy - the Milky Way, including the stars astronomically around us.

We are very fortunate in one sense. The Solar System is out towards the galaxy's rim, so we have a reasonably clear view through the veil of its stars into Deep Space, showing (with sufficiently powerful telescopes of different spectra) the Milky Way as just one of hundreds of thousands of galaxies.

And even if we had a telescope powerful enough, the furthest objects we could see would be 1.4 to 1.5 X 10^10 light-years away, because that number is the calculated age of the Universe in years, so light from anything beyond that distance has not yet arrived here. 

"I'm the only one that sees it that way." Because I'm the only one standing here.