John le Carré and Ian Fleming wrote novels about British intelligence operations. Their novels were very popular, and so were the main characters in them, who were British intelligence officers. So: If a British intelligence officer goes anywhere in the world, all he has to do is to introduce himself (tell who he is and what work he does-- an officer of British intelligence) and his work would be understood and he would be expected to be like one of the characters from the novels. So he would be recognized -- his job would be understood-- but he might not really be welcome, since his work is to be a spy. A "calling card" is a little card -- a business card, we usually call them -- with a person's name, company, and phone number.

The idea is that, before John le Carré and Ian Fleming made MI6 famous by their spy novels, people outside the UK (or even inside the UK!) didn't know that there was an intelligence branch of the British military called MI6. Because le Carré and Fleming made MI6 famous, a British intelligence officer (from MI6) can leave his "calling card" anywhere in the world and be confident that people will know who he works for even though they may not welcome him (because they might not like MI6).