What is magnification/power as it pertains to telescopes?

Magnification of a telescope is actually a relationship between two independent optical systems: the telescope itself and the eyepiece you are using. To determine power, divide the focal length of the telescope (in mm) by the focal length of the eyepiece (in mm). By exchanging an eyepiece of one focal length for another, you can increase or decrease the power of the telescope. For example, a 20 mm eyepiece used on a 1000 mm focal-length telescope would yield a power of 50x (1000/20 = 50). While a 10 mm eyepiece used on the same instrument would yield a power of 100x (1000/10 = 100). Since eyepieces are interchangeable, a telescope can be used at a variety of powers.

There are practical limits of magnification for telescopes. These are determined by the laws of optics and the nature of the human eye. As a rule of thumb, the maximum usable power is equal to 50-60 times the aperture of the telescope (in inches) under ideal conditions. Powers higher than this usually give you a dim, lower-contrast image. For example, the maximum power range on a 90 mm telescope (3.6 in aperture) is 180x-216x. As power increases, the sharpness and detail seen will be diminished. Higher powers are mainly used for lunar, planetary, and binary star observations. 

Most of your observing will be done with lower powers (6 to 25 times the aperture of the telescope in inches). With these lower powers, the images will be much brighter and crisper, providing more enjoyment and satisfaction with the wider fields of view.

Always start with your lowest magnification (longest focal length) eyepiece and work upwards from there. 

A 2x Barlow lens will double the magnification of whatever eyepiece you use with it while preserving its eye relief. For example: using a telescope with a 900 mm focal length with a 20 mm eyepiece will give you 45x magnification. Using the same telescope and eyepiece with a 2x Barlow lens will give 90x magnification. This would be the same magnification as a 900 mm telescope with a 10 mm eyepiece.