This article is from the Photographic Lenses FAQ, by David Jacobson with numerous contributions by others.
Aberrations are image defects that result from limitations in the way lenses can be designed. Better lenses have smaller aberrations, but aberrations can never be completely eliminated, just reduced.
The classic aberrations are:
* Spherical aberration. Light passing through the edge of the lens is focused at a different distance (closer in simple lenses) than light striking the lens near the center.
* Coma. Off axis points are rendered with tails, reminiscent of comets, hence the name. It can be shown that coma must occur if the image formed by rays passing near the edge of the lens has a different magnification than the image formed by rays passing near the center of the lens.
* Astigmatism. Off-axis points are blurred in their the radial or tangential direction, and focusing can reduce one at the expense of the other, but cannot bring both into focus at the same time. Think of it as the focal length as varying around the circumference of the lens. (Optometrists apply the word "astigmatism" to a defect in the human eye that causes *on-axis* points to be similarly blurred. That astigmatism is not quite the same as astigmatism in photographic lenses.)
* Curvature of field. Points in a plane get focused sharply on a curved surface, rather than a plane (the film). Or equivalently, the set of points in the object space that are brought to sharp focus on the film plane form a curved surface rather than a plane. With a plane subject or a subject at infinite distance the net effect is that when the center is in focus the edges are out of focus, and if the edges are in focus the center is out of focus.
* Distortion (pincushion and barrel). The image of a square object has sides that curve in or out. (This should not be confused with the natural perspective effects that become particularly noticeable with wide angle lenses.) This happens because the magnification is not a constant, but rather varies with the angle from the axis.
* Chromatic aberration. The position (forward and back) of sharp focus varies with the wavelength.
* Lateral color. The magnification varies with wavelength.