Magnification (Power) is calculated by dividing the focal length of the telescope by the focal length of the eyepiece. This means the shorter the focal length of the eyepiece is the higher power is will be. This also means a given eyepiece used in different telescopes of difference focal length will produce different magnifications.
Magnification is useful when viewing the moon and planets. Power is also useful when using a telescope terrestrially. But there are limits.
During the daytime, typically you will not be able to view at a distance at more than 60 power. (Spotting Scopes usually to not exceed 60 power). This is because as you increase the magnification, you increase the magnification of everything, including turbulence in the atmosphere. As a rule if a magnification produces a unstable image you probably will want to reduce the magnification a bit.
Astronomers use a term for the stillness of the atmosphere called “Seeing”. “There is good seeing tonight.” “There is bad seeing tonight.” “Seeing” is basically a relative measurement of the stillness or turbulence of the atmosphere. If the stars are twinkling, the seeing is probably not good.
When seeing is poor, less magnification is used to steady the view through the telescope.
A good practical rule-of-thumb is to figure about 50 power per inch of aperture of the telescope for telescopes under 6 inches of aperture.
For example, a 4.5 inch (114mm) Newtonian Reflector telescope will theoretically max out around 225 power, sometimes refered to as "225x". The practical limit is probably around 100-200 power for high power views of the planets and moon, depending on the “seeing” and the quality of the optics. You can put even higher power eyepieces in (This is how some inexpensive department store scopes advertise 300, 500 even 900 powers.), but the views will be unsatisfactory and useless.
In the above example you could theoretically reach the 225 power or even exceed it a little, if you have good optics and incredibly still atmosphere – a rare occurrence in most places.
When is Magnification Not Desirable
In astronomy, high magnification isn’t always desirable. When trying to locate an object, like a planet, you may want to use a low power eyepiece with a wider field-of-view to locate it, then switch to a higher power eyepiece to study it. Planets are relative small astronomical targets.
Deep Sky objects, like nebulae and galaxies, are very dim and sometimes very large. Deep sky targets are best viewed with low-power, wide-field eyepieces. As you increase magnification you will spread the light out decreasing the contrast by squares and conversely decreasing the magnification will increase the contrast and brightness of the view.
For example, if you cut the magnification in half, you will increase the brightness by 4.
Also some deep sky targets are large. For example the Andromeda Galaxy is 3 degrees in size which is six times larger than the moon appears at one half a degree. Most telescopes would not be able to view the entire Andromeda Galaxy without an extreme wide field.
Optically adjusting the magnification
There are a few optical devices that you can place between the eyepiece and telescope to modify the magnification. These are barlows and focal reducers.
Very simple barlows are magnification multipliers. These optics typically multiply the magnification of any eyepiece by 2, although 3 power barlows and other magnifications are available.
A barlow basically doubles the number of eyepieces available. For example, if you had a set of three eyepieces at 32mm, 25mm and 20mm, a 2 power Barlow would also give you the equivalent of a 16mm, 12.5mm and 10mm eyepiece respectively.
Focal Reducers, sometimes referred to as “field flatteners”, are usually used in astrophotography and function opposite of a barlow by making the magnification less. Higher end telescopes like Schmidt-Cassegrain and some high-end refractors can use a focal reducer.
For example, an Schmidt-Cassegrain telescope is typically an f/10 system, you can purchase an f/6.3 or f/3.3 focal reducer which threads onto the rear cell of the telescope, effectively turn that scope into an f/6.3 or f/3.3 system. The f/6.3 would be useful for both astrophotography and visual work. The f/3.3 would be for astrophotography only.