A color cast is a visible color tint to an image, usually referring to one that is unwanted. They occur when white balance is inaccurate or light is contaminated with a color, such as in the instance of bouncing from a colored surface. For example, in an image with a green color cast, neutral tones would have a green tint rather than being truly neutral.
If the color cast is due to white balance inaccuracy, it's an easy fix in post-processing software with white balance/tint sliders. If the cast came from lighting, like a flash bounced off a colored surface, shot through a gel, or mixed lighting, it can be a more in-depth fix involving selective color adjustments.