Any difference between the image of an object viewed through a riflescope and the ideal image of that object is called "aberration." Here are some of the more common types of aberration that you might hear about when optics are being discussed.
Chromatic aberration This is a color flare or color fringe along the edges of objects in the image.
Spherical aberration This occurs when light rays passing through the center of the lens do not focus at the same point as rays of light passing through the lens edges. The result is a low-contrast, soft-focus image.
Pincushion and barrel distortion This is the tendency of straight lines to "bow in" or "bow out" from the center of the image to its edges.
Astigmatism This is the inability to focus the image due to imperfections in the lens system.
Curvature of field The image is not flat. Straight lines appear to be bent.
It is important to recognize that no optical system can be completely free of aberration. All optical systems are a design compromise that minimizes some types of aberration while necessarily allowing others. Many of the lens elements in a riflescope are included for the purpose of correcting various types of aberration.
Aberration is not simply the result of imperfect lens grinding or improper design; some types of aberration are basically inevitable, due to the fact that different wavelengths of light focus at different points. Also, some types of aberration result from the characteristics of spherical lenses (lenses whose curved surfaces are ground with an equal-radius curvature). Some forms of aberration can be eliminated by the use of aspherical lenses.