Franking is the term for any marking that is placed on an envelope in order to qualify it for being sent. The most common franking is of course postage stamps.
However, the most common use of the term "franking" refers to the "Franking Privilege" where members of the United States Congress get to send job-related mail for free by signing (or using a rubber stamp of the congressman's signature in) the top-right corner of the envelope where the stamp would be. Franking is not actually completely free but instead each congressman gets an amount proportional to the cost of sending a first-class message to every address in each Congressman's district or state.
However, franking also has unintended consequences. You see, campaign materials can be sent out with this stuff--you know, "My opponent wants to kill all extremists--do you want that to happen?" Therefore, laws were passed banning this free mail for being used for campaign messages or for mass messages to be sent out within 60 days of an election. This, of course, mostly serves to lead congressmen to try to figure out how best to twist the wording of the law, in order to keep one of the major campaign advantages of incumbency.