From A Wiki of Ice and Fire
Hedge is a term that occurs in real world history, and not just for knights. In Westeros "hedge" is attached to various people, such as hedge knights, hedge teachers, hedge poets, hedge wizards. They are basically poor itinerants who have to sleep in the hedges as often as not, since they don't have a roof over their heads. George R. R. Martin has seen the term hedge used most frequently in Irish history, which is where he got it from.
Fifty, if he's a day, a hedge harp, and hard used by life.—Jaime Lannister, taking note of Tom of Sevenstreams