The image circle is the circular projection of light that a lens casts onto the film plane or sensor. Every optical design forms a round image because the elements themselves are round; the rectangular crop seen in the final photograph is just the portion the sensor records. The image circle must be at least as large as the diagonal of the sensor, or the corners of the frame fall outside the projected light and appear as black or vignetted regions.
For a 36x24mm full-frame sensor, the diagonal is roughly 43.3mm, and any lens marketed as full-frame projects an image circle slightly larger than that. APS-C lenses project a smaller circle (around 28mm diagonal) and Micro Four Thirds lenses smaller still. Mounting an APS-C lens on a full-frame body almost always results in hard vignetting in the corners, since the circle does not reach them; most full-frame bodies automatically switch to a cropped mode to compensate.
Tilt-shift and view-camera lenses have unusually large image circles by design. A standard 24mm tilt-shift for full frame might project a 60mm or larger circle, giving room for the lens to shift several millimeters off axis without darkening the corners. This is the entire point: shifting the lens lets the photographer move the framing within the projected circle to control perspective on architecture without tilting the camera. Tilting the lens reorients the plane of focus, taking advantage of the same oversized circle.
Medium-format lenses project an even larger circle to cover sensors up to 53.4x40mm or, for film, 6×7 and 6×9 cm. Adapting these lenses to smaller formats wastes most of the image circle but can deliver unusually clean corners on smaller sensors, since the area in use sits well inside the projection’s sweet spot. Some photographers exploit this when mounting old medium-format glass on full frame for sharpness with a vintage look.
The edge of the image circle is rarely a clean boundary. Light falls off gradually into mechanical vignetting, then drops sharply to nothing at the limit of the projection. Fisheye lenses in circular projection are an exception: they deliberately cast a circle smaller than the sensor, exposing the black surround as a stylistic choice. Diagonal fisheyes, by contrast, cast a circle just large enough to cover the corners.
Practical implications include adapter design (a Canon EF lens adapted to Sony E covers the same circle because the diagonal is similar; an APS-C EF-S lens does not), the use of speed boosters (which compress the image circle to a smaller sensor, gaining a stop of light and a wider field of view), and the corner sharpness of designs pushed close to their projection limit. Whenever a lens looks soft or dark in the extreme corners on a body it was not designed for, the image circle is the underlying explanation.