Astigmatism occurs when an optical system has a different power in one plane than at a right angle to that plane. When an object is on-axis, the two planes are identical (both are radials of the mirror or lens) so there is no astigmatism, if the element is properly made.
When an object is off-axis, the plane that passes through the object and the optical axis is called the tangential plane. The plane at right angles to it is called the sagittal plane. Depending on the optical system, the rays in the tangential plane may focus closer or farther than those in the sagittal plane.
Like spherical abberation, astigmatism may be a result of the particular optical design, or a result of grinding and figuring. The latter is especially true for optical windows and corrector plates where it is very easy to develop a slightly different curve in one direction than another.
Astigmatism is one of the easier abberations to detect at the eyepiece, as the image will rotate 90 degrees from inside of focus to outside of focus, as in the example above.