Rolling shutter is a phenomenon in digital imaging sensors. It is the wobbliness which makes the image kind of compress and squeeze, echo the movements of the camera, and is usually highly undesired effect. Rolling shutter and shaky camera is usually associated with lower-budget productions were stabilization systems, or other camera equipment like cranes, jibs or rigs are not used due to their high price. Camera sensors capture image by scanning it from for example top to bottom, and the inability to scan the image at the same moment in time is what causes the wobbliness. The rolling shutter effect is heightened if shutter speed is low, since each frame is exposured a bit longer and then gives more probabilities for the parts of the frame be temporally apart. Also using camera freehand is prone to produce rolling shutter due to natural vibration of the body movements, and also a zoom lenses are known to have this effect since they magnify the shakiness. The upper part of the image is captured in right time, but the lower part of the image is actually captured in a bit of delay. This is a mathematically predictable distortion, and can be corrected using right algorithms. All the information in the image is there, but it just needs to be put in the right order.
Some programs offer tools for removing the rolling shutter effect, thus increasing the image quality greatly. After Effects has a great Rolling Shutter Removal tool which removes the rolling shutter practically completely, and if a smoother camera movement is desired, also the Warp Stabilizer is a viable choice. It has the option to smooth the camera movement as well remove the rolling shutter effect.