The word is related to the Greek word for "goat," and one legend tells that the aegis is from the skin of a pet goat which belonged to baby Zeus; later, Zeus used the shield made from the goat's skin in his battle against the Titans. You can read more about the legend of the aegis at Wikipedia.
Athena's aegis bore the image of the head of Medusa the Gorgon, as you can see in the image below, a statue of Athena by the sculptor Phidias: