A postcard ID is a little code that uniquely identifies a postcard in the system. It is composed of two parts: two letters (the country code) and a number. The postcard ID is used by the recipient to register the received postcard in Postcrossing.
For each address you request to send a postcard to, a postcard ID will be given to you. This means only official cards have postcards IDs (postcards that you have privately swapped with other users cannot be registered).