Field curvature is an aberration (distortion) in the image of some optical instruments (such as some telescopes), in that it brings the image to focus at a curved-shape rather than a flat-shape. If the instrument incorporates a flat sensor, then the best focus that results is either at its center, or forming some ring concentric to the center, the rest of the image being fuzzier.
A Schmidt telescope has considerable field curvature, a choice in its design to gain other advantages. Its spherical mirror produces spherical aberration, and a lens (the Schmidt corrector plate) reduces the spherical aberration but leaves it with substantial field curvature. The design's advantage is an easier-to-manufacture mirror, and a good image despite a short focal length giving it a large field of view suitable for surveys. I believe special curved photographic plates were used with them, but the CCDs more recently used are generally flat. I read that one current strategy is an additional lens which reduces the field curvature (a field flattener lens).