What is Wrapping wires through a metal ring called? ?

It's an EMI (electromagnetic interference) filter. The "ring" is a ferrite toroid that filters out common-mode interference.

EMI (Electromagnetic Interference) Filters, also known as RFI (Radio Frequency Interference) Filters, basically are passive electronic devices that are used to suppress conducted interference that is found on a signal or power line. Electromagnetic Interference (EMI) is unacceptable electromagnetic emissions, natural or man-made, which result in the degradation or malfunction of electronic or electrical equipment. Radio Frequency Interference (RFI) is detrimental electrical energy in the frequency range, which is for the specific transmitted radio frequency. Major sources of EMI and RFI include microprocessors, switching power supplies, AC motors, and electrical power cords (which basically act as an antenna).

As mentioned previously, an EMI Filter is a passive electronic device (comprised of multiple components) for suppressing conducted interference found on any signal or power line. An EMI Filter will suppress the interference created by other equipment and the interference of the module or system itself, with the desired result being improvement to the immunity from EMI signals in the surrounding setting. EMI Filters can be found both in plastic as well as metal housings, in stand-alone, desktop or module configurations.

An EMI Filter works by presenting a significantly higher resistance to higher frequency content. In other words, the low pass design of the EMI Filter (the combination of shunting capacitors and series inductors) results in the restriction/impeding of the flow of high frequency signals, effectively shorting it to ground. The final result of the EMI Filter is that it reduces and attenuates the unwanted signal strength, thereby having a minimal effect on other components or devices. EMI Filters are gauged by specifications including insertion loss, voltage rating, and current rating. In addition, there are numerous approval authorities and specifications, including UL, CSA, VDE and military specification.