From https://en.wikipedia.org/wiki/Franking:

Franking privilege

“Privilege” franking is a personally pen-signed or printed facsimile signature of a person[11] with a “franking privilege” such as certain government officials (especially legislators) and others designated by law or Postal Regulations. This allows the letter or other parcel to be sent without the application of a postage stamp. In the United States this is called the “Congressional frank” which can only be used for “Official Business” mail.[12][13]

In addition to this type of franking privilege, from time to time (especially during wartimes) governments and/or postal administrations also authorize active duty service members and other designated individuals to send mail for free by writing “Free” or “Soldier’s Mail” (or equivalent) on the item of mail in lieu of paid postal franking, or by using appropriate free franked postal stationery. In the United States, unless otherwise designated, such mail is serviced by both the military and civil postal systems that accept them as First Class letter mail.[14]

History of the “franking privilege”

A limited form of franking privilege originated in the British Parliament in 1660, with the passage of an act authorizing the formation of the General Post Office. By 1772, the abundance of franked letters represented lost revenue of more than one third the total collections of the Post Office.[21] In the 19th century, as use of the post office [22] increased significantly in Britain, it was expected that anybody with a Parliament connection would get his friends’ mail franked.

In the United States, the franking privilege predates the establishment of the republic itself, as the Continental Congress bestowed it on its members in 1775. The First United States Congress enacted a franking law in 1789 during its very first session. Congress members would spend much time “inscribing their names on the upper right-hand corner of official letters and packages” until the 1860s for the purpose of sending out postage free mail. Yet, on January 31, 1873, the Senate abolished “the congressional franking privilege after rejecting a House-passed provision that would have provided special stamps for the free mailing of printed Senate and House documents.” Within two years, however, Congress began to make exceptions to this ban, including free mailing of the Congressional Record, seeds, and agricultural reports. Finally, in 1891, noting that its members were the only government officials required to pay postage, Congress restored full franking privileges. Since then, the franking of congressional mail has been subject to ongoing review and regulation.

The phrase franking is derived from the Latin word “francus” meaning free. Another use of that term is speaking “frankly”, i.e. “freely”. Because Benjamin Franklin was an early United States Postmaster General, satirist Richard Armour referred to free congressional mailings as the “Franklin privilege.”

A U.S. Congressional franked mailing

The use of a franking privilege is not absolute but is generally limited to official business, constituent bulk mails, and other uses as prescribed by law, such as the “Congressional Frank” afforded to Members of Congress in the United States. This is not “free” franking, however, as the USPS is compensated for the servicing of these mails by annual tax-funded appropriations against which each Member is given a budgeted amount upon which he or she may draw.