Barkness can refer to one of a few different things. It began life as Scott Hammack's almost-apocryphal quote, "Darkness Schmarkness go to Barkness", which was mentioned in Mini-Darkness.
Later, the Cans series made Barkness more famous by portraying it as MegaZeux's equivalent of Hell, where MZXers pay for their sins. Chuck is sent to Barkness on more than one occasion, mainly to do battle with Robert.
The most recent appearance of Barkness is the DigitalMZX subforum of the same name, though at least one forum admin has a habit of changing the name of said subforum several times a month (previous titles have included "UNITED STATES OF BARKNESS" and "FROZEN COW INDUSTRIES"), but the forum has colloquially been known as Barkness.