Yup, that's right, in clicker training the click is used
after the desired behaviour, or one close to it, is performed. The click is positive reinforcement rather than a command - it's like saying 'Well done, that's right'. It's used rather than just verbal praise or a treat alone as it's a more consistent and distinctive signal, and it's easy to quickly click the very instant the desired behaviour is performed, so the animal is clear which behaviour is the one being reinforced. Otherwise, by the time you'd got a treat to them, they might be doing something else, and you'd instead end up accidentally reinforcing that behaviour rather than the one you wanted - by clicking before giving the treat they know which behaviour it was that got them the food reward. Once the animal understands what you're wanting them to do, a verbal command and/or hand signal is added, and the click gradually phased out (you can see her using verbal commands and signals in some of her other videos:
http://www.youtube.com/watch?v=-7ojKuMmw7Y). Clicker training does require the animal to actively try to work out what is required.