Astigmatism is a type of aberration (distortion) in the image of an optical instrument (such as a telescope) such that there are points on the focal plane that are focused along one direction (along some line) but not focused along the direction perpendicular to the first. A point source is focused into a short fuzzy line segment, and a cross-shaped source aligned with the direction that is focused shows two opposite arms in good focus, and the other two fuzzy. Such astigmatism could be deliberately caused by incorporation of a cylindrical lens or mirror, e.g., asymmetric around the optical axis yet symmetric to a plane through the axis. Glasses are often shaped to reduce this kind of astigmatism in human eyes.
Optical systems symmetric around the optical axis also generally suffer from astigmatism: it can be due to manufacturing flaws but there is also inherent astigmatism: this type of combination of good and bad focus occurs in points away from the center of the image (or more specifically, that at the optical axis), the good and bad directions being on lines through the center versus concentric rings that cross the line, but I'm not sure which of those typically has the better focus: it may depend upon how far from the center. Telescope designs often must trade off between astigmatism and other aberrations (and complexity). Three-mirror anastigmat telescopes aim to reduce astigmatism as well as other aberrations, at the cost of incorporating a tertiary mirror.