Focal length is the distance in mm from the optical centre of a lens to a point where a subject at infinity appears in sharp focus - usually usually the surface of a piece of film or a digital camera's sensor.
In the days when 35mm film cameras ruled the roost, we all got used to what the various quoted focal lengths of lenses meant. For example, we knew that a 28mm lens gave a wide-angle view while, say, a 300mm telephoto lens offered a much narrower angle of view that brought far-away subjects much closer.
These days, with digital cameras using different and generally smaller sized sensors, it can be harder to get a feel for the angle or field of view of a given lens. When you consider that some compact cameras have lenses with focal lengths as short as 6mm, it's almost impossible to know what sort of field of view that lens offers.
To get around this confusing situation, camera manufacturers often quote their lenses or cameras as having a 35mm equivalent focal length. This is an indication of what the angle of view of a lens would be if it were scaled up to work on a 35mm film camera.
So, when you read that a compact camera has a zoom lens covering a range of 24-180mm… that isn't actually the actual focal length of the lens - it's the 35mm equivalent. This system of using a focal length equivalent works well for most of us as it makes comparing models of cameras and zoom ranges with different sized sensors so much easier.
Focal length magnification and crop factors
So, for compact cameras we have the whole focal length question pretty well sorted, but what happens if you use old 35mm SLR lenses on a modern digital SLR, most of which have smaller sensor areas than a frame of 35mm film? What happens then with things like field of view?
Well, in these situations manufacturers will quote a crop or magnification factor to indicate how much of the field of view a sensor can cover. With the popular APS-C sized sensors used in Canon and Nikon DSLRs, the crop factor is around 1.6 and 1.5x respectively.
This means if you use a 28mm lens on a Canon SLR camera that has a 1.6x crop factor, you need to multiply the focal length of the lens by 1.6; this gives us the focal length of 45mm. So, a 28mm lens when used on an APS-C format SLR will behave more like a standard lens on an old 35mm camera.
Other cameras with different sized sensors have different crop factors. For example, Four Tthirds and Micro Four Thirds cameras have a crop factor of 2x, which means that a 40mm lens has the same angle of view as a 80mm lens on a 35mm camera.
Unfortunately crop factor formulas don't work the other way round. If you were to use a lens designed to work on a camera with a 1.6x crop factor with a full-frame 35mm sensor, the lens won't project a full image onto the sensor and you would see dark vignetting in the corners of any images recorded on the camera.