I'm not an optician, but I do have astigmatism...
Basically, astigmatism is a problem with the shape of the eyeball. The optician who diagnosed mine described it as the eyeball being rugby-ball-shaped, rather than spherical. This results in print, etc looking blurry even when short/long sightedness have been corrected for.
If you have a copy of your (or your DDs) glasses prescription, there are usually a few numbers for each eye.
The first is the short or long sightedness bit: + for longsighted, - for shortsighted.
The astigmatism is usually the second one: + for an eye shaped like an "upright" rugby ball, - for "lengthwise" rugby ball, iyswim...
E.g. my right eye prescription is -3.25 (shortsighted), -2.25 (astigmatism).
Hope that helps (and that an optician comes along soon with a better explanation than mine)!