As defined on Wikipedia, aegyo (애교) is “a cute display of affection often expressed through a cute/baby voice, facial expressions, and gestures.” The definition found on the blog Eat Your Kimchi expands on that, specifying that “aegyo body language can be as simple as a small pouty lip, a hand fluttering to cover the mouth when shy, or as complex as multiple foot stops in union with shoulder gyrations.”

Although such behavior might be more commonly associated with women, men are also known to behave like that. It is usually employed as a form of fanservice.

Example of usage:

"Oh man, I can't get enough of watching SNSD on variety shows. Sunny's aegyo never fails to brighten up my day."

Definition reference: Wikipedia (https://en.wikipedia.org/wiki/Aegyo)

Eat Your Kimchi (http://www.eatyourkimchi.com/aegyo-in-korea/)