Huge topic... here's a quick and dirty: There are two main categories of lenses, prime lenses and zoom lenses. Prime lenses have a fixed focal length, eg 50mm; that is, they cannot change their field of view, and to get more or less area in the picture you have to physically move the camera. Zoom lenses, through a rather more complicated optical process cover a range of focal lengths in one lens, eg 70mm-300.
They can also be subdivided based on their focal length. In the days of film, a 50mm lens was considered a 'normal' lens, that is, it most closely approximated what was seen by the human eye. Because most DSLRs have sensors smaller than a 35mm film negative, there's a magnification factor, and on most DSLRs, a 35mm lens would be considered normal. Anything above 'normal' is generally regarded as a telephoto lens, whether zoom or prime, and anything below is regarded as a wide-angle lens. Those which cover the 'normal' range are sometimes referred to as 'normal' or 'mid-range' zooms.
Therefore, a 70-300mm lens would be a telephoto zoom, and a 12-24mm would be a wide-angle zoom. A 28mm prime lens would be considered wide-angle and a 105mm prime would be considered telephoto. Typically wide angle lenses go as low as about 10mm (VERY wide) and telephotos up to about 400mm (high magnification). T
When you're talking about lenses the focal length or "mm" number is simply an expression of how wide the field of view is for that particular lens. A 10mm can see an area many, many times wider than a telephoto. The other number you'll see is the aperture, usually preceded by an "F". This is a representation how much light the lens will admit, the smaller the number (eg f2.8) the more light the lens will allow to hit the sensor.
There's a great deal more to it, including Depth of Field, hyperfocal distance, as well as many specialty types of lenses, but that gives you an idea. In short, if you want to make objects appear closer to the camera, use a telephoto, or long focal length. If you want to see a large area, than a wide angle or short focal length.