Coil whine is a phenomenon in electronics where electromagnetic coils within an electrical circuit exhibit a high pitched sound as electricity passes through the circuit. Typically, this is most often heard in high performance computer components such as graphics cards and processors, but is actually very common in other electronics such as fluorescent light ballasts.
While annoying and sometimes a bit scary, coil whine is simply a result of sounds made as electricity passes through electrical coils. This is typically a result of poor engineering as these sounds can be minimized by utilizing coil dampening techniques. Rest assured however, no damage will occur to your system.