Interesting, I've been working on an article on freeshaping and Schutzhund training. To me the "free" in freeshaping refers to two different things. First it means that you are "free" of any tool or gimmick other than your mark and your reward. No leashes or collars, no props or tools needed (unless what you are shaping is the dog interacting with a "prop" like perch training, retrieves, jump technique...). No corrective devices (not because correction is bad, but it's not part of freeshaping). The second aspect of it being "free" means that it promotes a certain learning style within the dog. The dog learns to be more "free" himself. The dog is not dependent on the handler for lures and excess cues, nor stressed or anxious because it was patterned trained and something didn't happen in the right order. The dog is more free thinking and able to try things on his own in order to find the "right" (desired) behavior that earns the reward. Pure freeshaping is really standing their and waiting for the dog to offer the behavior (or the step toward the behavior) that you want, so freeshaping = problem solving.
Freeshaping usually works well with backchaining, but you can freeshape a simple behavior and not be backchaining, and you can backchain behaviors using lure/reward or classical conditioning or escape training. The most common place I see backchaining and freeshaping used together is what people call the "purely positive" retrieve.
I like to use freeshaping across venues (obedience, agility, Schutzhund, rally....) as much as possible because I like my dog to be clear-headed and problem solving without excess help from me or conflict created by me. Some dogs take better to this training style than others. It's almost like you have to initially train the dog to understand the training style, and then you have to use it on a fairly regular basis for the dog to keep up with it. As much as I love and prefer freeshaping, I also use a LOT of lure/mark/reward type training, I use all sorts of corrections in all three phases, and I also use pressure/escape training (the latter of which I believe is much like freeshaping, a form of training I find very valuable and need my dog to understand so I make a point of using it for certain behaviors).
I think freeshaping requires a lot of patience from the handler. I believe it helps a handler become a better trainer because it forces the handler to break down behaviors in ways the dog will understand, and it places absolute importance on the timing of the mark/reward (and on the flip side, I think prong collars are a great tool and I prefer them over e-collars because it forces the handler to learn correct line handling, what type of correction is appropriate, timing of the correction, and how to use directional corrections).
What I see from my dog that I've made a much better effort at freeshaping is a dog that more clearly understands behaviors. Just because a dog DOES a behavior or a chain doesn't mean he really understands what he's doing and exactly what he needs to do to earn the reward. Also, the behaviors I've freeshaped happen to be behaviors where my dog has always been correct and consistent, haven't had to go back and fix or polish this or that because with freeshaping, you simply don't move on to the next step unless the dog is correct in the step you're on (but again, this implies some skill on the part of the handler, knowing what IS correct and how to break down these steps for the dog). Two things I'm freeshaping right now are the send out for Schutzhund and the 2x2 weave method for agility. The last thing I've freeshaped was teaching my puppy to speak/bark (that would be an example of something that is simple, not a behavior chain that is backchained, I just stand there with the reward until the dog makes a noise, then mark/reward, then after several reps of this I up the ante and wait for the dog to make a louder noise...then up the ante more until the dog must actually bark for the reward).
I guess a very simple example of freeshaping would be the A-frame. Most people would simply leash their dog, guide it over, and praise or throw a toy on the other side. Nothing wrong with that, works just fine (and with most dogs I'd probably do just the same). But say I want to "freeshape" this behavior. I take the dog free of any "hardware" and go to the area of the A-frame. This is the dog's first interaction with the A-frame, so when the dog goes over to sniff it, I mark/reward. After the dog has figured out "I'm getting rewarded for messing with this A-frame", he decides to climb it. Now I only mark and reward for climbing it. Then we progress to mark/reward for climbing up and over the other side. Then he needs to go over and back to earn a reward. At this point I should say that I use freeshaping mostly for understanding the behavior and correctness. Once the dog does the whole thing - going out, over, and back - and clearly understands that is why he's getting rewarded, I'll do something that puts the dog in a higher state of drive which increases speed. I once saw in a video clip Ellis saying that dogs don't really understand getting rewarded for a fast behavior and not getting rewarded for a correct but slow behavior and I tend to agree with this. When I want a FAST behavior, I get the dog in a higher state of drive beforehand. So anyway, back to freeshaping the A-frame. I taught a dog this way while my friends led their dogs over the A-frame by the leash and gave a toy on the other side. The result was one dog who was instantly terrified of the A-frame and refused to do it, and another dog that liked the A-frame and was willing to interact with it but didn't really understand that the behavior = go over, come back, and get reward, so he was inconsistent (stopping at the top and running back for the toy, going around it, going over it but coming back around). The issue most people have with freeshaping is that it takes a lot of time and patience at the beginning. Once it "clicks" I find that the dog really takes off and doesn't need to be cleaned up after the fact, but it can take a while to "click". So, it might take me three sessions of freeshaping to get my dog doing the A-frame but after three sessions I can heel him over, tell him "hup" without any other cue, lure, or reward present, and have him go over and back to me whereas one friend's dog won't go near it and the other friend's dog will go on it but now has tried all these wrong things and needs to be fixed for those three sessions. Again this is just supposed to be a simple example, in the grand scheme of things going over the A-frame is not a major issue or accomplishment.