The film's title can be interpreted on multiple levels.
On a literal level, the film’s title relates to some of Turing’s most important work, but it’s at best peripheral to the film’s plot. The term “imitation game” comes from a paper Turing wrote in 1960 called "Computing Machinery and Intelligence,” where he asks "Are there imaginable digital computers which would do well in the imitation game?" Turing then goes on to describe a game that is really a test to determine if computers can actually think.
Turing describes it as a simple party game involving three players. Player A is a man, player B is a woman and player C (who plays the role of the interrogator) is of either sex. Player C is unable to see either player A or player B, and can communicate with them only through written notes. By asking questions of player A and player B, player C tries to determine which of the two is the man and which is the woman. Player A's role is to trick the interrogator into making the wrong decision, while player B attempts to assist the interrogator in making the right one.
Turing then argues that the game can prove the presence of (artificial) intelligence if a computer could take the role of Player A and make player C guess wrongly just as many times when an actual human being is sitting in for Player A.
Examined more closely, one also could interpret the title as a metaphor for Turing's inability to truly understand and relate well to others. Perplexed by the tangled web of social interactions, intimations and subtext, Turing often discusses his difficulty with human interactions. It’s worth noting that an earlier film on Britain’s WWII code-breaking efforts was also called Enigma, the title of The Imitation Game’s source book, and the producers did not want audiences to confuse their film with the previous one.