The balay--apparently standing on the ground in this case-- holds the rope at a loose tension while a climber works up the cliff. As long as anchors (pitons traditionally) are secured to the rock, ...that the climber puts in (or uses)and the rope placed in it is shorter than the distance to the ground the climber cannot fall all the way down--he'll only fall the distance between himself and the last anchor, below that anchor--and the belay will hold him.
It works well--when the climber uses enough anchors. In this case, apparently Mr. McAfee got too confident....and didn't use enough...getting more than 15 feet above his last anchor. That is not the balay-man's fault.
Only 30 feet too. What a shame.
Here's an illustration of what I mean (this is from a climbing site, the balay in this case was standing away from the rock face, and un-anchored, causing the problem in the 2nd pic). You can see though, assuming the balay is well anchored, if the climber fell, the anchors in the cliff would prevent catastrophe:
