After visiting the DMZ and searching around online, the only answer seems to be "to prevent defection." Supposedly this was done after the 1984 defection of a Soviet tourist that ran across the border. The idea that two guards face each other so one doesn't run, and a guard facing the North to lookout for other defectors.
If this is truly the case, how does the North justify it to their guards? I have a hard time believing for 30 years they have been telling guards to watch out for their comrades escaping the paradise of the DPRK.
As with anything you hear about North Korea, you have to take that information with a grain of salt. "To prevent detection" seems like a pretty reasonable explanation, right? But that's not it at all. This is the Kim family after all that we are talking about.
What is actually going on is a staring contest, with pretty huge stakes. The garrison charged with the duty of guarding the border are the absolute most trusted members of the DPRK military, and there is really no concern about them defecting. They are fully prepared to hold their hair back to make for a cleaner cut if Glorious Leader decides that they were to be beheaded. All for the greater good!^1
So anyways, as I said, there are high stakes here. In 1984, Kim Il-Sung decided that he wanted to liven things up and instituted this contest. The garrison is made up of forty members working in pairs, and the schedule was made up so every member of the guard has guard duty an equal number of times with each other member^2 . During their 8 hour shifts, they must stare directly at each other. The first one to break eye contact, the other guard gets 2 points. Any break of eye contact after that results in 1 point. Scores are tallied at the end of the shift, and the winner earns one 'Kim'.^3 Before 1993, the winner in 'Kims' was simply that, the winner. This changed in 1993 under Kim Jong-Il, who created a conference system, so two groups of 20 would see each other much more often, and only members of the other conference once during their year long rotation, until the finals held in December where the top five of each conference had to face off in a double elimination tournament.^4
What are the stakes you ask? Well, the winner gets to have him and his family smuggled into Japan to visit Disney Land Toyko for a week. The runner up is provided with a years supply of two-ply toilet paper.^5 The guard with the lowest point score had to serve as Glorious Leader's foot-stool for the next year, but rumor is that Kim Jong-un has really upped the ante, and now requires that the loser's entire family provide a complete set of human furniture, but we're breaking the 20 year rule by a lot, so I can't get into that.^6
^1 My Journey on the Line, by Ganz Betrüger, 2004 (He is a Swiss journalist who spent a year living at the North Korean DMZ building, and built a real raport with the guards. A very unique look at life there)
^2 US Military Intel Brief 2749-B(3.S), 1985, Declassified in 2010
^3 Glorious Leader, Glorious Layup: Sport Culture in the Hermit Kingdom, Charles Taylor, Adolf Dassler, 2012
^4 US Military Intel Brief 61257-P\4.4, 1996, (Still classified, part of the Bradley Manning leaks)
^5 G. Betrüger, 2013 Revised edition
^6 But Will They Match the Drapes?: The Impact of Border Guard Behavior on North Korea's Luxury Furniture Market, by Bob Kaufman and Gene Rosenberg, published in Furniture and Cabinet Maker's Quarterly, Summer, 2013
EDIT: WHILE IT MAY SEEM THAT NOTHING THAT HAPPENS IN NORTH KOREA IS TOO CRAZY TO BE TRUE, THIS ISN'T (as far as I know). IT WAS AN APRIL FOOLS POST! CHECK THIS THREAD OUT FOR MORE INFO!