In a telescope or camera, the focal ratio is the ratio of the focal length divided by its aperture. It's a dimensionless number and therefore the calculation has to be performed with the focal length and aperture expressed in the same units of measure.
The f-number tells you how 'fast' or 'slow' a scope is. A fast scope has a low f-number and is good for imaging faint objects, while a slow scope with a high f-number is better for lunar and planetary imaging.
For cameras, these ratios are standardised. Common focal ratios or f-numbers are: f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16 and f/22. Telescope focal ratios are not standardised but usually are of the order of f/10 for Schmidt-Cassegrain scopes, f/8 for refractors and f/5 for Newtonian reflectors.