Moscow Centre is a nickname used by John le Carré for the Moscow central headquarters of the KGB, especially those departments concerned with foreign espionage and counterintelligence. It arises from use by Soviet officers themselves, and le Carré probably just utilised the nickname to gain greater credibility for his books.
The part of Moscow Centre most often referred to in le Carré's novels is the fictional Thirteenth Directorate headed by Karla, the code name for a case officer who has risen and fallen from political favour several times and was at one point 'blown' by the British in the 1950s. Karla and George Smiley meet while Karla is in prison in Delhi at this time, with Smiley trying to persuade Karla to defect during an interrogation in which Karla gave away nothing. Karla refused these advances and eventually returned to favour in the USSR, masterminding the Witchcraft/Source Merlin operations supporting the mole Gerald in the Circus. Karla possesses a cigarette lighter given to Smiley by his wife Lady Ann; he took this during Smiley's interrogation.
In Smiley's People, a murder in London sets in motion a chain of events that lead to the defection of Karla; it is implied that without him, Moscow Centre will be considerably weakened.
Karla was played in the TV adaptation of the novels by Patrick Stewart.