Magnification is the relationship between an object's real size and its size on film. If, for example, you take a picture of a US 25¢ coin (roughly 24mm in diameter) such that it creates a 24mm wide image on-film, the magnification is equal to 1. (Also written 1:1.) If, instead that coin takes up 12mm on the film's frame, you have a 1/2 or 1:2 magnification ratio.
The magnification formula is mainly used by macro shooters, though it also has other applications. For example, the Field of View calculation has magnification as one of its factors.
The magnification of a given lens, given its focal length and the distance to the subject is calculated as:
where f is the focal length of the lens, and s is the distance from the optical center of the lens to the subject. (Roughly equivalent to the camera-to-subject distance, except for closeups.) Both values must be in the same unit, such as millimeters.