MALS wanted a more detailed explanation of backward-shaping, so I'll do my best.
I was first introduced to backward-shaping through the work of Karen Pryor, an animal trainer whose book Don't Shoot the Dog is one of a very few books I think pretty much everyone should read. Karen Pryor teaches positive reinforcement and clicker training, and while the book is marketed as a dog-training book, it has broad-based applications for teaching pretty much any kind of animal - including humans.
Backward-shaping involves two things. First is breaking a complicated task down into bite-sized bits, giving the trainee a high chance of success. The other is working from the unknown to the known, so that instead of starting with the part of the task the trainee knows well and progressing into successively less well known parts, you start with a part the trainee doesn't know and move from there into parts the trainee knows better and better.
Most people do this quite naturally with some tasks. When we teach a child to make cookies it's pretty common to start by teaching them to roll the dough into balls and put them on the tray. From there you progress backwards to having them add the fun ingredients like the chocolate chips, and from there to running the mixer, and from there to measuring ingredients. Each time you bake cookies, you start the child on something they don't know (measuring), and then progress into something they know better (mixing) and then into something they know well (making dough balls).
With other things, like pieces of music or karate katas, backward-shaping is counter-intuitive, but the principles work the same. You break the whole into bite-sized bits, something small enough to be taught in a single session, the same way you would if you were teaching (or learning) front-to-back. But instead of teaching the first portion of the sequence first, you start with the last one - the ending chords of the sonata, or the final pass of the kata. Once that's well established you back up to the next bit, and teach it. The trainee then learns the new bit and flows from that new section into the ending section that they already learned. So the training sequence for something that's been broken into five sections would look like this: 5, 45, 345, 2345, 12345.
One major advantage to backward-shaping is that the trainee is always working towards what they know, which tends to end training sessions on high notes, which is good for morale on both sides. One disadvantage is (as noted in the prior post) most students aren't used to learning this way and tend to be weirded out the first time they encounter it. My experience would tend to indicate that it's a pretty valuable technique when you can find people who are comfortable working this way, and I would encourage people to try it and see how it works for them.