‘Tether’ can be used many ways in climbing. In general, ‘tether’ as a noun means something that keeps things attached. In climbing that could be something as simple as a rope, but it could also refer to equipment that the climber wears which allows him to attach to other things.

It means that two objects are connected by a rope. "The climber was tethered to the mountain by a long rope."

You may have seen images of mountain climbers with ropes running between them. I believe this is what the word means.