You need alternating current to operate a transformer. (It does not work with DC). Transformers are required to step up and down the voltage which is required to transport electric energy in an economic way. frequency's of 40 to 400 Hz work fairly well for transformers, and the choice with in this range must have been fairly arbitrairly. But one can imagine that the number 60 is inspired minutes of a clock, wher as the number 50 is inspired by the decimal number counting (a half of 100). By the way 60 Hz is slightly more efficient. A US transformer often has a hard life in Europe. For weight saving the frequency of installations in airplanes are historically 400Hz. Transformers can be much smaller this way.