Shielded cable can be used to reduce electrical noise in the form of electromagnetic interference (EMI) generated by nearby equipment.
Shielded cable will usually be a multiconductor cable that will be surrounded by braided copper, a conductive foil, or some other conducting material. The shield can reflect energy and pick up the noise and conduct it to ground. Here is a video that gives a visual example of what noise is and what the shield does to alleviate it.
Should you ground one or both ends of a shield? There isn’t a clear answer to this question. In a perfect world, the shield should be connected to ground at both ends, creating the maximum conductive tunnel around the conductors. However this requires that “ground” be the exact same reference on both ends of the cable and in cases where cables go from one location to another, chances are there will be some potential difference between the two grounds at the two ends of the cable which will create a “ground loop” allowing some current to flow from one end to the other. Once the shield begins to carry current, it is no longer an effective shield against noise.