Does anyone know the origins of the term?
This is a matter of some debate, and the truth is that you can pick up any number of photography books (or visit any number of photography websites) and read a variety of answers to this question, the most common of which tend to be:
As with many historical 'facts,' the truth is quite a bit messier than many of these sources would seem to indicate, and the real reason that we use 'f-stops' today to some extent defies a quick explanation.
The Wikipedia F-Number article actually has a rather complete (and well cited) history of how we got here, but some of the 'high points' are:
The major settings (on the square root of two sequence: f/1.4, f/2, f/2.8, f/4, f/5.6, f/8 ...) used to be physical detents (stops) on the aperture adjustment control ring. Finer adjustments were always possible, but tactile feedback for settings in between traditional stops is a relatively new development.
The "f" part refers to the convention for naming the aperture-to-focal length ratio: f/2, f/2.8, f/4, and so on, where the variable "f" represents the focal length. A 50mm lens set to f/2 will have an effective aperture of 25mm diameter, while a 100mm lens set to f/2 will have a 50mm effective diameter.
Given equal transmissivity, the same ratio of aperture size to focal length will allow the same rate of light accumulation upon the film or sensor for lenses of differing focal lengths.
"Always" is a bit misleading, I suppose -- back in the days when you actually had to install a different aperture disk, you would only have had access to whatever settings you had in your kit, and I've used antiques that only had the click-stops available -- the detent was strong enough that you couldn't use the tweens so you'd have to make fine adjustments in development or printing.