Where I grew up we used to use this term to refer to the style of beard/sideburns someone gets where the sideburns are trimmed into a thin line that may connect to a goatee/moustasche of the same thinness. I've never really heard anyone from anywhere else really call it that. It looks cool on people with a dark complexion, but I think it looks kind of white-trashy on white guys.
-similar to "edge up" but refers specifically to facial hair
Shit, man nice edge job!
-Yeah, it's tight, right?