Since the earth takes slightly more than 86,400 ( = 60 * 60 * 24 ) formal seconds to complete one rotation, a leap second is added occasionally to slow up the clock. This is the wacky part: for a moment, the seconds of the "official" time are 60.
Near end of "normal" minute: seconds go ...,57,58,59,00,01,02,... Near end of "leap second" minute: seconds go ...,57,58,59,60,00,01,...