The power of an eyepiece is found by dividing the focal length of your telescope by the focal length of the eyepiece. For example, a 20mm eyepiece on a 2000mm telescope (2000/20) gives you 100 power (100x). This makes objects appear 100 times closer to you through the telescope than they appear to your unaided eye. The same 20mm eyepiece on a 1000mm focal length scope (1000/20) gives you 50x. The longer the telescope focal length, or the shorter the eyepiece focal length,the higher the power - but the dimmer the image.
Highest Useful Magnification
Any telescope is theoretically capable of unlimited magnification. As power increases,however, image brightness on extended objects (nebulas, galaxies) decreases, as you'll see in the section on "exit pupils." Point sources (stars), on the other hand, do not become dimmer. As you get to 50x or 60x per inch of aperture, some faint extended deep space objects can become too dim to see. Thus, while an 8" telescope is theoretically capable of a maximum useful deep space power of 480x (60 x 8), that much power is often usable only for splitting close binary stars.
More than 60x per inch of aperture is sometimes possible for planetary observing with small aperture telescopes (under 4"-5"), since a small scope looks through less of our turbulent atmosphere than a large one and therefore is less affected by unsteady seeing. Unfortunately, the exceptionally good seeing that allows such high magnifications is rare.
During average seeing conditions (the kind you find nine nights out of ten), 25x to 30x per inch of aperture is a more sensible power for binary star and planetary observing. It is at this power that the resolution of a scope most closely matches the resolution of your eye and images are sharpest. This gives you a highest useful power of about 200x to 240x with an 8" scope on an average night, 100x to 120x with a 4" scope, etc.
Globular clusters and the smaller nebulas are best at about 12x to 15x per inchof aperture, while 8x per inch of aperture is usually best for finding galaxies and observing large nebulas. Once found at low powers, the contrast of smaller galaxies and nebulas against the sky background can often be improved by increasing the magnification to the 15x to 20x per inch of aperture range.
Lowest Useful Magnification
The lowest power usable from a dark sky observing site is about 3x to 4x per inch of aperture - for viewing open clusters and rich field scanning of the Milky Way star clouds. An eyepiece with still lower power has an exit pupil (the beam of light coming out of the eyepiece) larger than the pupil of your eye. A portion of the exit pupil falls on your iris, instead of entering your eye, effectively reducing the aperture (and brightness) of your scope.