Field rotation is the apparent rotation of a celestial object in the field of view of a telescope during the course of the night. All objects in the eyepiece field or on the camera’s image will move in arcs. It’s usually either ignored or not noticed for visual observations, but cannot be ignored for photography.
It happens when you are using an altazimuth mount or a misaligned equatorial mount. In these cases, all the stars will appear to move around the point or star that is being tracked. Field rotation will occur unless the mount is exactly aligned to counteract the earth's rotation.
Field rotation can be visualized by thinking about what happens when a constellation or the moon rises, transits and sets. From northern latitudes, Orion will rise on his side with his left shoulder (the one north of Rigel) highest. As he crosses the sky he will reach and transit the meridian, when both shoulders will be the same height. When he sets, the right shoulder (Betelgeuse) will appear highest. It’s like he’s climbed the dome of the sky, reaching the top and then goes down the other side. The angle of his body changes during the course of the night, first tilting to the east, then tilting to the west. Similarly, the moon will rise with the Sea of Crises (Mare Crisium) edge leading upwards, the Ocean of Storms (Oceanus Procellarum) following and lower. Both of these dark areas will appear about the same altitude when it transits, then the Ocean of Storms will be higher than the Sea of Crises as the moon sets. Again the tilt changes as the moon moves across the sky. Both examples show field rotation with your head and body acting like an altazimuth mount.
Because of field rotation, visual directions north, south, west and east will change relative to the top and bottom of the eyepiece during the night. Usually this is not important but you should be aware of it.
On photos, even if tracking on a star is perfect, unless the mount itself is perfectly polar aligned, there will be some degree of field rotation. Only the center will show pinpoint stars or sharp detail. Towards the edge of the field of view, all stars will show arcs concentric with the center. If you are guiding a photograph and using a star off-center or outside the field of view for guiding, then the arcs will be concentric on the guide star.
Because of field rotation, no altazimuth mount is suitable for long-exposure astrophotography. Only a properly polar-aligned equatorial mount will eliminate field rotation.