While many people are all about the telescope, the eyepiece often comes as an afterthought. For a serious astronomer, this can be somewhat of a mystery as the eyepiece can go a long way in making viewing more enjoyable or, at the least, more varied.
The first question many people have with eyepieces is 'how powerful is it?' Well, there is no single answer to that question as eyepiece power is directly related to what telescope it is being used with. To find eyepiece power, simply divide the telescope's focal length by the eyepiece's focal length. Example: a 10mm eyepiece in 1000mm scope (1000 divided by 10) results in 100x power. In a 500mm scope, that same 10mm eyepiece results in 50x power (500 divided by 10).
Another thing to consider about eyepieces is the size of the opening through which you look. Old-fashioned eyepieces resemble peepholes when of short (powerful) focal lengths. Now, thanks to computer design and ever-increasing creativity, some short focal length eyepieces can have massive openings, providing bay window-like views to the universe.
A final consideration of eyepieces is their angular field of view. Needless to say, the wider the field, the better. Unfortunately, for those super-wide, 90+ degree fields, you'll be paying a lot of money and using eyepieces that seem to weigh as much as bricks.
Lastly, good eyepieces come in two sizes: 1.25 and 2 inch diameters. The small, .965 eyepieces bundled with some department store telescopes are a sure sign of a junk telescope as no modern company with any degree of self-respect would market such a product.