The f-number is a ratio, not a measurement: focal length divided by the diameter of the aperture opening. A 50mm lens with a 25mm opening is at f/2. Because it is a ratio, f/2 admits the same light on any lens at any focal length, which is what makes the scale universally comparable.
The standard sequence — f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16 — looks arbitrary but each step halves the light of the one before. The odd-looking numbers are powers of the square root of two, because light passes through an area, and halving an area means dividing its diameter by roughly 1.41.
Two practical notes. Smaller f-numbers mean larger openings, which trips up nearly everyone at first. And most lenses are not at their sharpest wide open — stopping down two or three stops from maximum usually hits the sweet spot, before diffraction begins softening things again past f/11 or so.