The focal ratio is the ratio of the focal length of the telescope related to its aperture. It’s calculated by dividing the focal length by the aperture (both in the same units). For example, a telescope with a 2032 mm focal length and an aperture of 8 in (203.2 mm) has a focal ratio of 10 (2032/203.2 = 10) or f/10.
It’s variously abbreviated as f-stop, f/stop f-ratio, f/ratio, f-number, f/number, f/no., etc.
Smaller f-numbers will give brighter photographic images and the option to use shorter exposures. An f/4 system requires only ¼ the exposure time of an f/8 system. Thus, small focal ratio lenses or scopes are called “fast” and larger f/numbers are called “slow.” Fast focal ratios of telescopes are f/3.5 to f/6, medium are f/7 to f/11, and slow are f/12 and longer.
Whether a telescope is used visually or photographically, the brightness of stars (point sources) is a function only of telescope aperture--the larger the aperture, the brighter the images. Extended objects will always appear brighter at lower magnifications. The main advantage of having a fast focal ratio with a visual telescope is that it will deliver a wider field of view than slower f-numbers.