Leap seconds are an outgrowth of the post-World War II development of increasingly accurate clocks based on the regular vibration, or "resonance," of atoms as they pass through a magnetic field. In 1958 an atomic second was defined as the time it takes for an atom of cesium 133 to tick through 9,192,631,770 cycles.
At that point atomic time and astronomical time are approximately the same, with the traditional astronomical second defined as 1/86,400th of a "mean solar day," the average time between two consecutive noons.
The trouble is that the heavens behave more capriciously than cesium. Also, the length of Earth's day is increasing by about two milliseconds per century because of the tides, whereas today's atomic clocks, unaffected by cosmic events, tick away with an accuracy within one second for every 20 million years.
Now who knew? And who cares? Apparently, there are those who say this difference affects things like computers and satellites. I'll bet not as much as the Y2K crisis.