Many advanced cameras will have interchangeable lenses, and learning what lenses can do for you will greatly increase your ability as a photographer.
There are two types of lenses: Prime and Zoom. A zoom lens allows you to zoom in on a subject by changing the focal length of the lens. A prime lens has a fixed focal length (no optical zoom).
Why would someone choose a seemingly more restrictive prime lens? The biggest advantages to prime lenses are the quality for their cost and open apertures (Prime lenses are also lighter). Cheap prime lenses can generally take images with quality as high or higher than expensive zoom lenses, and they almost always have a larger maximum aperture, allowing you to shoot at faster shutter speeds in low-light situations to avoid blurs, or to create very shallow depth of field.
Focal Length is the distance from the center of a lens to its focal point. A lens with a focal length under 50mm is referred to as wide-angle, and a lens with a focal length over 50mm is referred to as telephoto. These lenses offer a wide angle of view and greater magnification, respectively.
Your choice of focal length will affect the size of distant objects, the size of the frame for each photo, and the difficulty of getting a sharp photo without a tripod (a telephoto lens will magnify the effect of a shaking hand).
Effective Focal Length is calculated by multiplying a lens focal length by the crop factor of a camera's sensor. Cameras without a full-frame sensor will crop the image because they only "see" the center part of the light entering the lens. For example, if your sensor is half the size of a full-frame 35mm sensor, it will only record light at the center of the lens, and that capture of the smaller area of light creates a photo where objects are seen twice as large, and the effective focal length is twice as high.
Fast and Normal are words you may see when purchasing a lens. A fast lens is one with a large maximum aperture (low f-stop number) because it allows more light to hit the sensor so a faster shutter can be used. A normal lens simply means that objects will look natural and not distorted (the focal length will be around 50mm).
Check out my comparison of the Canon EF 24-105mm f/4 L vs. Canon EF 24-70mm f/2.8 L.