Telephoto lenses. They have a narrower field of view than wide angle lenses; this normalizes the relative distance and size between objects placed at different distances if compared with wide angle lenses: closest objects will appear similar to farer ones because, due the narrow field of view, far objects will cover a large portion of the angle and the
distance will appear compressed. They are normally used to photograph subjects you are not able to approach filling the frame with them, as in wildlife or sport photography. But this use would be very reductive. Telephoto lenses can be used in landscape photography for example,
filling the frame with a single element or selecting a portion of landscape; or you can take advantage of the appearance of compressed distance and play with different layers of landscape compositions or exaggerate the density of a pattern. The most known aesthetic characteristic of telephoto lenses is the
shallow depth of field they can achieve at a given distance (the compressed distance enhance and magnify the out of focus area), which is great for isolating subjects from the background, very useful for portraits.
Prime and zoom lenses. While the prime lenses have a fixed focal length, zoom lenses have a variable one.
Prime lenses tends to be smaller and, generally, they offer a better optical performance than zoom because the light passes trough less optical elements, even if nowadays the difference is not that big as it used to be. Diaphragm aperture thou, will always be bigger with prime lenses and it may varies in the zoom lenses, according to the focal length it is used. On the other side,
zoom lenses are practical for the kind of photography in which you have to constantly switch from one focal length to another. So which one should you choose? As always, it depends on you and your photography, but remember to stay functional. For the kind of photos I make, I prefer prime lenses and I think that the best zoom are my feet (because I like better the change of relative perspective than magnifying the whole image), while for some one else it is more practical to carry and use 3 zoom lenses than 6 or 7 different prime lenses...
Next, special lenses. Don't miss it!
Telephoto lenses. They have a narrower field of view than wide angle lenses; this normalizes the relative distance and size between objects placed at different distances if compared with wide angle lenses: closest objects will appear similar to farer ones because, due the narrow field of view, far objects will cover a large portion of the angle and the distance will appear compressed. They are normally used to photograph subjects you are not able to approach filling the frame with them, as in wildlife or sport photography. But this use would be very reductive. Telephoto lenses can be used in landscape photography for example, filling the frame with a single element or selecting a portion of landscape; or you can take advantage of the appearance of compressed distance and play with different layers of landscape compositions or exaggerate the density of a pattern. The most known aesthetic characteristic of telephoto lenses is the shallow depth of field they can achieve at a given distance (the compressed distance enhance and magnify the out of focus area), which is great for isolating subjects from the background, very useful for portraits.
Prime and zoom lenses. While the prime lenses have a fixed focal length, zoom lenses have a variable one. Prime lenses tends to be smaller and, generally, they offer a better optical performance than zoom because the light passes trough less optical elements, even if nowadays the difference is not that big as it used to be. Diaphragm aperture thou, will always be bigger with prime lenses and it may varies in the zoom lenses, according to the focal length it is used. On the other side, zoom lenses are practical for the kind of photography in which you have to constantly switch from one focal length to another. So which one should you choose? As always, it depends on you and your photography, but remember to stay functional. For the kind of photos I make, I prefer prime lenses and I think that the best zoom are my feet (because I like better the change of relative perspective than magnifying the whole image), while for some one else it is more practical to carry and use 3 zoom lenses than 6 or 7 different prime lenses... 
