An eyepiece can be thought of as a magnifying glass that enlarges the image produced by the telescope. The telescope system is only complete with an eyepiece.
The comparison with a magnifying glass can be taken a step further, in that the focal length of the eyepiece determines the magnification. Magnification results from the ratio of the focal lengths of the telescope and the eyepiece according to the formula:
Magnification = focal length telescope / focal length eyepiece
A telescope set-up should therefore include at least three eyepieces, so that observation with different magnifications is possible.
Deciding which magnifications will be most useful also depends on what you wish to observe:
In practice, the maximum magnification is usually limited by air turbulence (known as seeing).
Another important indicator for eyepieces is the apparent field of view. Eyepieces with an apparent field of view of more than 60° mean that no border interrupts your field of view: the object being observed is surrounded by a star field, you have the impression of being in space. In addition, these eyepieces offer a pleasant viewing experience.
An example of eyepieces with a narrow field of view and a rather more difficult viewing experience are the classic Plössl eyepieces, which are often included in the scope of delivery of telescopes. However these eyepieces also have their strengths: since they contain only 4 lens elements, they offer a high-contrast image without stray light. This is ideal for observing bright objects at high magnification: details of the Moon, planets and the Sun - the latter of course only with a solar filter!