The eyepiece that you use in your telescope determines what magnification or power that you can see. Eyepieces are usually described by their "focal lengths". A 4mm eyepiece is an example of a very short focal length, and will deliver high power. A 40mm eyepiece is a long focal length, and will render low power . These two examples are the approximate extremes of both ends of the typical scale. The typical eyepiece(s) that come with a new telescope are likely to be 25mm or 10mm, and yield 40x to 100x magnifications. It should be noted that parfocal eyepieces can be interchanged without the need for refocusing (so it is worth sticking to one brand of eyepiece).
Eyepieces also come in different barrel diameters, 0.965", 1.25" (31.7mm), and 2". Eyepieces are available in different basic designs. Some are suited for specific situations. Here are the most common types:
Panoptics & Naglers
The standard diagonal on most telescopes are "ok" , but they will absorb some light.
Don't make the mistake of assuming that all things are better viewed with high powers. Most general viewing of comets or deep sky objects are done with modest 25x to 80x power.However, to view Planets like Jupiter and Saturn high power is recommended. The moon, and many double stars can require the maximum that your telescope's optics can deliver. Upwards of 200x power is usual.