Fast-roping is the art of descending (quickly) from a hovering helicopter to the ground using a heavy rope. These two videos show the basic principles behind fast-roping...
In this first video you can see that there are no harnesses, no clips - it's just a rope and a good pair of gloves:
At the end of the following video you can see how thick a typical fast-roping rope is, and get a perspective from inside the helicopter:
The rope has to be that thick for two reasons. First, if it is too thin it is hard to grip and causes too much friction (even with gloves). Second, if it is too thin, all the wind from the prop's down wash will whip it around. Worst case scenario is that a thin rope somehow whips into the main rotor or the tail rotor.
The gloves need some thought as well. Braking your descent with your hands means friction and therefore heat. Too much heat can be a real problem, so thick or padded gloves are preferred. You do not want to fast-rope with a pair of thin gloves or bare hands.
What can go wrong? Three things:
1) You can see in the first video that people who are fast-roping are vulnerable to small arms fire, both as they exit the helicopter and as they descend the rope.
2) People who are new to fast-roping can misjudge their speed and land hard. This can also happen if the backpack weighs a hundred pounds or the gloves are too thin (the following 17-second video may contain one expletive at the end, but contains an excellent example of a fast-roping error):
3) If fast-roping into an unsecured landing zone, there is the possibility of an unfriendly welcoming party: