To start, I am 39 years old, and not too hip, so younger people may have a different feeling for the word. Additionally, I am American. Edgy is a person or style that pushes boundaries, usually cultural/traditional/moral/ethical. The term's positivity/negativity are based on context. "My girlfriend rides a Harley and is covered in tattoos - I love edgy girls!" and "Last night, John walked out of that restaurant without paying - he's a little too edgy to hang out with." If you don't like someone pushing on a particular boundary, it's a criticism. If you think the boundary is someone a good, brave person should push, it's a compliment.