An accidental wiping of the eyebrow during a bowl movement.
Usually occurs when someone has to expell a Massive Shit and a lot of sweating occurs. During the wipe, a finger mildly brazes the turd being wiped. Then, the person wipes his/her eyebrow to clear the sweat of a job well done, leaving a smear of fecal matter on the eyebrow or forehead. Thus, a BROWN BROW...
Jimmy had to unload a big one earlier. He must have not looked in the mirror because he didn't notice the brown brow he came out of the shitter with
Brown-Brow: Brown-brow is the result of someone having fecal matter smeared across their forehead in the typical "unibrow" fashion.
My brother Jonathan pissed me of so I gave him a brown brow.