Since the protagonist is a spy, spy training is very important both to his job and to the plot of the novel. Alec Leamas is a veteran spy who is beginning to lose his skills; he is recruited for a final mission to plant false information. His training comes in handy in several ways, mainly in the development of "assets," or unaware persons who are of use in his mission. This requires many skills of deceit, fast thinking, and intimate knowledge of both the asset (who is usually scoped out before contact) and surrounding places, people, or events. The use of these skills allows authenticity, and since people don't expect to be lied to so blatantly, trust is established and the asset is encouraged to take actions that benefit the spy's agenda.
Leamas was sweating. Peters watched him coolly, appraising him like a professional gambler across the table. What was Leamas worth? ... Leamas was too much off balance to monkey about. He was a man at odds with himself, a man who knew one life, one confession, and had betrayed them.
(Le Carré, The Spy Who Came In from the Cold, Google Books)
This scene establishes Leamas as a powerful actor; Peters, a veteran recruiter who has turned many defectors, believes that Leamas is shaken and on edge from his betrayal of his beliefs. Instead, Leamas is patiently and deliberately fostering a false impression in Peters, allowing Peters to believe what is convenient while telling as many lies as possible. By allowing Peters to believe that he is controlling the conversation, Leamas creates a false impression of himself, and is seen as trustworthy.