Purpose
A telephoto acts like binoculars for your camera. It brings distant objects closer, allowing you to focus on a specific object in the wider viewing field.
Telephoto vs. Zoom
Telephoto and "zoom" lenses are not the same. A telephoto has a single fixed focal length measured in millimeters (28mm, 50mm, etc.); a zoom lens has the ability to bring an object up X number of times (4x, 10x, etc.).
Uses
Using a telephoto lens, photographers can not only bring distant objects closer but also manually blur the background around the central object to achieve more interesting pictures.
Considerations
For more control over your images, acquaint yourself with the different types of telephoto lenses. You might need a different lens to photograph flowers than you would for capturing sports action or birds in flight.
Bottom Line
Remember that not all "long" lenses are telephotos, but all telephotos have the same basic function: bringing distant objects closer, for more focused and more interesting pictures.