Free climbing (climbing without the aid of a rope but using it for protection in the event of a fall) is a quite forgiving hobby! I've fallen hundreds of times while free climbing and lived to tell the tale :).
The distinction between free solo climbing and free climbing is frequently a point of confusion -- especially in news articles!
Here is a good article which goes a bit in to the most audacious free soloing link-up in Yosemite: http://www.nytimes.com/2012/06/16/sports/rock-climber-alex-h...
What is special about this attempt is that it appears they will successfully climb every pitch, in order, without using the ropes to ascend.
These guys are falling a lot on their way up. Don’t they want to climb the whole thing without falling? Well, that would be nice, but in this case, it’s okay for them to fall. They’re trying to “redpoint” the route, which means each climber has to climb each pitch without falling. So, if Caldwell is climbing pitch #11, and he falls 40 feet from the start of the pitch, he lowers down to the start of the pitch and starts over until he finishes the pitch cleanly. Then that pitch is considered free climbed, and he moves onto the next pitch. Since each pitch can take a half hour to an hour to climb, you can imagine how ridiculous it would be to climb all the way up to, say, Pitch #17, and if you fell, lowering 1,700 feet to the ground and starting over.
[1] http://www.alpinist.com/doc/ALP26/first-ascent-bachar-yerian