I recently watched this film, and I thought it deserved all the plaudits and its success at the Oscars (the most boring of all awards ceremonies). At its heart I think it's a commentary about the power and importance of language. This becomes particularly obvious when Bertie is sitting watching a film of Hitler speaking and mesmerizing his audience.
The monarch's job then, as now, is to be a talking head. As Bertie's father George V (Michael Gambon) shouts at one point "This family has been reduced to that basest of all creatures - we've become actors!". The film explores what it must be like to be forced to become a public speaker and effectively be unable to speak.
I also came across a radio interview in which Colin Firth discusses the film and the real George VI. He is incidentally an excellent speaker, and is managing to make a career out of gracious awards acceptance speeches at the moment: