Reverse psychology is based on the simple idea that sometimes when you tell people to do one thing, they will choose to do some other thing. As you may have guessed, this is not actually a sub-branch of psychology; the phrase was apparently coined by a professor at Harvard Business School in the 1920s to make his marketing lectures sound more interesting. While it is still largely a marketing term, it has leaked into common usage, and has been used by the masses since at least the 1950s.
The classic example of reverse psychology is the salesman telling his mark "well, that model is probably a little too expensive/refined for you; let's look at something a little cheaper/simpler". The idea is that by putting the customer on the defensive from the start, they will try to prove that they aren't cheap, stupid, or tasteless by spending more. The term is used in many different contexts, and it is unsafe to assume that an author or speaker is using it in any particular sense. Stores that do not overtly display their goods, limited edition items, and even TV shows with abrasive leading characters (such as Hell's Kitchen) may be considered forms of reverse psychology.
In less technical contexts, you may hear parents say that they are using reverse psychology on their kids when they say things like "I know you couldn't possibly eat any more vegetables!", rather than "you had better eat some more vegetables!" In addition, any variation of the idea you want what you can't get qualifies as reverse psychology, and there are web-pages that will be glad to tell you how to apply this to any area of your life, from child rearing to getting promoted; apparently dating is a popular subject for reverse psychology. If you choose to visit any of these sites, keep in mind that they are telling you to manipulate others for your own benefit. This may be okay in the case of children (YMMV), but generally it is not a brilliant idea to lie to and manipulate others if you plan on having a long-term relationship with them, in business or love.