A spotting scope is a small telescope that has been modified for use by day. A spotting scope differs from an astronomical telescope in several important ways. First, a spotting scope always produces an upright image whereas a telescope used in astronomy may produce a reversed image or even an upside down image (not a problem for astronomy). Second, a spotting scope is much smaller in size than an astronomical telescope, mainly for the sake of portability. Third, a spotting scope is a lower magnification instrument than a telescope, since the atmosphere by day does not allow the high magnifications used in astronomy. Fourth, a spotting scope is mounted on an ordinary photo tripod, but a telescope for astronomy requires a very specialized mount, often unsuitable for daytime use. Lastly, many, if not most, spotting scopes are waterproof and fogproof - a rare feature in an astronomical telescope.
Spotting scopes are used anytime you need more magnification than a binocular provides. Spotting scopes are widely used for birding, surveillance, hunting, and viewing landscape, wildlife, ships and other distant objects. Spotting scopes are also used for scoring targets on rifle, pistol and archery ranges and they can also be used to some astronomy. Last, but not least, spotting scopes are also used to take long distance pictures with a variety of cameras.
Most spotting scopes are labeled with three numbers. The first two numbers represent the magnification range and the last number is always the size of the front lens. For a 15-45x60 model, then, you have a spotting scope with a zoom magnification range of 15-45x with a front lens of 60mm diameter.