Most historians concur that the term first came into wide use in the U.S. Military during the Vietnam War. However, the exact origin of the term is lost.
My friend Robert States disagrees with that. Robert was stationed in Germany from 1962 through 1966 and says that they used the term "Klick" all the time to denote the European "Kilometer." So, its possible the term originated in Europe, and migrated to U.S. Military use elsewhere, such as Vietnam.
Some military historians believe that the term originated in Vietnam with the Australian Infantry. As the story goes, infantry soldiers would navigate by bearing (compass direction) and would measure distance by pacing (this was, of course, prior today's magical GPS devices). In order to keep track of distance, one or two "nominated" soldiers would count their paces. About 110 paces on flat land, 100 paces down-hill, or 120 paces up-hill would equal 100 meters. The soldier would keep track of each 100 meter "lot" by moving the gas regulator on the Australian L1A1 rifle, one mark. After moving it 10 marks (1000 meters), the soldier would signal the section commander using hand signals, then indicate movement of 1000 meters by lifting the rifle and rewinding the gas regulator with a movement of the thumb, resulting in an audible "click."
Who knows? The story may not be true, but it sure sounds nice.
In "military-speak," the term "click" (spelled with a "c" instead of a "k") is used when sighting-in a weapon, such as a rifle. On most weapons, one "click" equals one second of arc, or -- in other words, one inch of distance at one hundred yards. So, moving the site adjustments of the rifle "one click" will change the point of impact one inch for a target 100 yards away, two inches for a target 200 yards away, and so forth. The term comes from the clicking-sound made by the sight adjustment knobs as they are turned.