What camera are you using or intending to own? Each different format (size of film or digital sensor) dictates a different "normal" lens focal length. A Digital Rebel, Rebel XT, 20D, and 10D all use a digital sensor with a size known as APS-C. They all use about a 31mm focal length as a "normal" lens. A 35mm film camera or a full-frame digital camera uses a 50mm lens as a "normal" lens. Lenses shorter than "normal" is considered wide-angle, and lenses longer than "normal" are considered telephoto.
There are two basic types of lenses. One is the "prime" lens, or one with a fixed focal length. The other is a zoom lens - one which can be adjusted to a range of focal lengths.
All modern lenses have an adjustable iris (like the iris in your eye) that can change the amount of light that enters the camera body to make an image. With a larger opening, more light gets to the film/sensor. The opening is usually defined as a ratio, using f-stop numbers. The standard numbers are f/1.4, f/2.0, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, and f/32. The smaller numbers relate to wider openings and are called "faster" because you can use a faster shutter speed with the wider opening. The higher numbers are called "slower".
Longer focal lengths (telephoto) can be used to take a photo of something far away, as if you are using a telescope. Shorter focal lengths can be used to take a photo of a wider subject without moving back (or if you can't move further back). This is the first thing that most folks think about when trying to choose a lens. However, there's an even more important (to the creative photographer) reason to choose different focal lengths for an image. Here's a link to another thread in these forums where I described this to a few folks and there are some examples there too: https://photography-on-the.net/forum/showthread.php?t=94147
Hope all this makes sense and gets you a little closer to understanding what you asked about.