A Farley File is a file of all the people that a politician (or other big shot, I suppose) has met and might be likely to meet again. Filed by name, it lists the basic information about each person, and most importantly, any information that the politician picked up in earlier meetings with that person.
The purpose of a Farley File is to remind the file-holder of the basic personal information of the person he is meeting with, and allow him to keep up a friendly and personal front with all his contacts -- a politician can't remember everything about all the people he meets, but common politeness requires you to remember the name of a person's spouse and children, their nickname, whether or not e smokes, drinks, and what e likes for lunch (most people recorded in the file won't need this much detail; the amount is determined by how much contact the politician is likely to have with this person in the future, and how bad his memory is).
This type of record is named after James Farley, Franklin D. Roosevelt's campaign manager. Farley used it for his own political career, and later when he managed Roosevelt's.