The origins and history of 'A wise old owl' are vague, however its meaning isn't, basically it would be told to children in an attempt to to teach the child the virtue of being quiet!
The lyrics of 'A wise old owl' poem are derived from the saying 'a wise old owl' based on an owl's behaviour of watching and patiently waiting when hunting its prey.
Legends concerning the owl are recorded in Greek, Celtic, Native American and Aborigine mythology.
The owl is is especially associated with wisdom in Greek mythology being linked with Athena, the Goddess of Wisdom.
Athens is named from the Goddess Athena and its emblem is the owl.
The owl was, for many years, viewed as a sinister bird only hunting at night when only evil spirits and witches were abroad - hence the connection with as a Witches Familiar!
A wise old owl - "Children should be seen and not heard!"