In more words, this is the little-known story (unknown -- even in its native England -- until only very recently) of Alan Turing, a mathematics genius and somewhat of a social misfit who largely cracked the unbreakable Enigma Code of the Germans, which is believed to have been central to the Allies winning WWII, shortened the war by two years, and saved up to 14 million lives. But the story is more than about that -- though that alone is riveting -- as it tells Turing's personal story, as a homosexual at a time in England when that was a crime. How he dealt with that and how it was dealt with by the British helps round the film out to much more than a great spy thriller.
There's some nice humor that fits impeccably out of the dialogue, and several twists and turns. So, I shall say no more. Other than, again, it's quite wonderful.
This is the British trailer. Like the U.S. one, it focuses more on the spy code angle, than gives a full sense of the film, but it does a better job of it.