Depends on exactly whose symbolism you are using.
Going back to ancient Greece, the Owl represented Athena - who was the daughter of Zeus and Metis. When Zeus learned that Metis was pregnant, he devoured her because he was suddenly terrified of the offspring overthrowing him on account if prophecy stating Metis would bear children smarter than the current gods.
This caused him a massive headache and Hephaestus grabbed a labrys to split Zeus's head open - and out jumped Athena, fully armed.
Athena was one of the most revered of the deities. She was, effectively, the ideal woman in both beauty and wit. She came to represent Democracy and her symbol was the owl.
As for the spider…
The Roman poet Ovid describes a competition against Arachne and Athena in the art of weaving. Ovid claims Arachne won - but there are other accounts of the same contest which vary. As a consequence for insulting the gods, Athena turned Arachne into a spider.
https://en.m.wikipedia.org/wiki/Owl_of_Athena
https://en.m.wikipedia.org/wiki/Arachne
Taking a less "aliens rule us" look at this symbolism, I would say that it means "mortal issues are of no concern here." The trivial tasking of the day - the daily grind/weave, are not issues significant to the discussions among the pantheon - the leaders and pillars of society.
There is a good and bad way to interpret this symbol, as with most of them.