What is focal-length? Are focal-length and zoom synonymous? How does the focal length of a photo affect it? Are there common uses for different focal lengths, and how can I decide what to use when?
Focal length is a measure how the lens focusses the light into a point. When light enters a 50mm prime lens, the light converges into a point the camera sensor after 50mm.
In addition the focal length determines the magnification of the object you photograph. A long lens (e.g. 300mm) magnifies the images a lot (useful for birding) while a short (wide angle) lens (e.g. 20mm) is useful for indoor pictures or landscapes.
Zoom usually means the focal length of the lens can be changed.
Focal length is the more techy way of talking about zoom (so that 3x optical zoom on a compact camera really means the focal length at its longest will be three times that at it's shortest, or widest).
You can use longer focal length to fake perspective, as the human mind is used to seeing pictures at a 35mm equivelent focal length of about 50mm.
If you're using a a modern DSLR you then get the crop factor (sometimes mis-described as a focal length multiplier), but for a camera with an APS-C sized sensor, you have a crop factor of 1.6; and if you have a 100mm lens attached to it, then it will have the same field of view as a 160mm lens on a 35mm camera; in reality, the focal length is still 100mm though.
The focal length of an optical system is a measure of how strongly the system converges (focuses) or diverges (defocuses) light.
In a single lens objective, the focal length is the distance to the film plane, but since most objectives are a rather complicated set of lenses it's not that simple.
That's rather technical, but the most interesting characteristic of focal length is that it's one of the decisive factors in how the angle of view of your lens is. The longer the focal length is, the narrower the field of view. The other decisive factor in the angle of view is the size of the film or sensor.
Lenses with a fixed focal length are also called primes, and lenses with a variable focal length are called zoom lenses.
Focal length is the distance from your lens to your film (or sensor). Depending on your focal length your picture is either zoomed in or zoomed out (or normal size when the focal length is usually 50mm).