Pretending to be stupid is a very old comedy device. The Greeks called it eiron, and irony comes from the same word. The Socratic method in philosophy also depends on it in the form of Socratic irony.
The idea is to unsettle the assumptions of your dialogue partner by questioning or simply not sharing his basic assumptions. This unsettling can be satiric (to show up the other person as stupid) or dialectic (by denying the assumption to find new truths).
For example, in Ali G's sketch DANGEROUS, Ali, a stupid street kid character created by Sacha Baron Cohen, interviews a professor from the National Poison Information Centre about drugs. Ali's pretended stupidity ("Does Class A drugs absolutely guarantee that they is better quality?") elicits a response that makes drugs look like any other consumer article.
Pretending to be less intelligent than your prospect is a field of pretending to be stupid that is exploited by sales people. As in most fields, the most successful people really need to be quite intelligent. However, if you are selling something you need your prospect to feel that he is in control. Therefore it can help to know how to pretend to be stupid. The most successful people tend to be very intelligent about pretending to be stupid without anyone realizing, particularly when their prospect is of above average intelligence, or is himself trained in pretending to be stupid sales techniques.
This mode is akin to the satirical tradition of supposedly naive observers, such as Oliver Goldsmith's supposedly Chinese letter-writer in 18th-century London, in The Citizen of the World, and others, including Montesquieu's Persian Letters.
It could also be a good tactic in a ways of hiding your power in were it may be a military strategy. For example, an enemy spy could act stupid to seem not like a threat, or for someone to be subtle in their manipulations, such as psychopaths.
See also