Very similar to carpet burn but obviously hapens when a rope runs through your hands. Now this might not seem like a common occurance but when you do a lot of climbing or caving then there is a large potential for receving this injury.

When you belay someone there are two ends of the rope passing through the belay device. If the person falls then their weight comes on the belay device and you must hold the correct rope, the rope that will halt the person from falling. This is known as the live rope. If you hold the rope on the wrong side of the belay device most devices won't work and the person will fall. The rope will rapidly run through your hand causing severe rope burn. Your partner may hit the ground and break bones or even kill themselves.

Allways pay attention to which rope you are holding whilst belaying!.

dwardu informs me that a very frequent form of rope burn happens while sailing... a very common occurence for rope to slip between hands powered by wind on a huge sail...