In Greek Mythology Athena is the goddess of wisdom, and her patron animal was the owl.
I recently took my wife on a falconry day handling birds of prey in Rutland and part of it was a session with owls the falconer burst that bubble and told us it IS a myth as Owls are not that bright -
As birds of prey, owls have huge eys, which stare and appear very knowing. in addition, they move their heads slowly, as though in thought, so give an impression of being 'wise'.
There's also an historical connecton with the magical and mystical... Merlin was depicted with an owl always at hand and I'm told the Harry Potter series of movies also employs the birds...
Additionally, their superior nocturnal eyesight and hunting skills adds to the "knowing" reputation...