Field Curvature, also known as “curvature of field” or “Petzval field curvature”, is a common optical problem that causes a flat object to appear sharp only in a certain part(s) of the frame, instead of being uniformly sharp across the frame. This happens due to the curved nature of optical elements, which project the image in a curved manner, rather than flat. And since all digital camera sensors are flat, they cannot capture the entire image in perfect focus, as shown in the below illustration:
In a simple field curvature scenario like above, the light rays are perfectly focused in the center of the frame, at Image Plane A (where the sensor is). Since the image is curved, sharpness starts to drop as you move away from the center, resulting in less resolution in the mid-frame and much less resolution in the corners. The circular “dome-like” image in three dimensional form is shown to the right of the illustration. If the corner of the image is brought into focus, which would move the image plane closer (Image Plane B), the corners would appear sharp, while mid-frame would stay less sharp and the center would appear the softest. The effect of field curvature can be very pronounced, especially with older lenses.