The definition of aw shucks is a type of behavior that is characterized by appearing or sounding shy, socially awkward or unsophisticated.(adjective)
An example of aw shucks is something you would say when you dropped a glass, or something you would say when someone gave you a compliment you weren't sure you deserved.
See aw-shucks in Webster's New World College Dictionary
See aw-shucks in American Heritage Dictionary 4