The Aegis as stated in the Iliad is the shield or buckler or breastplate of Athena and Zeus, famously bearing Medusa's head, which, according to Homer was fashioned by Hephaestus.
The modern concept of doing something "under someone's aegis" means doing something under the protection of a powerful, knowledgeable, or benevolent source. The word aegis is identified with protection by a strong force with its roots in Greek mythology and adopted by the Romans; there are parallels in Norse mythology and in Egyptian mythology as well, where the Greek word aegis is applied by extension.