The earth's rotation rate formally defined in 1956 by the International Committee on Weights and Measures as the length of the tropical year 1900 (calculated from the standard epoch of January 0, 1900 at 12 hours Ephemeris Time) being precisely 31,556,925.9747 seconds, or 365.24219879 days of 86,400 seconds each. This was determined using the 1898 Tables of the Motion of the Earth on its Axis and Around the Sun calculated by the American astronomer Simon Newcomb.
Since 1967 one second of time is defined as International Atomic Time (TAI) with a duration of exactly 9,192,631,770 cycles (that is, a frequency of 9.192... GHz) between two hyperfine levels of the ground state of a cesium-133 atom.With this precision, the rotation rate of the earth (measured by Very Long Baseline Interferometry using quasars) slightly varies, and in fact seemed to consistently slow down. Enter the leap second.
When the Universal Time Coordinated (UTC) second and the measured second using the earth's rotation vary by more than 0.9 seconds, an addition "leap second" was added (either on Jan 1st or Jun 1st). Since 1972 we've had 27 leap seconds, each adding a discontinuous bit of time and helping create confusion to precise measurement systems such as GPS and computer networks.
The leap second is no more. Late this year the International Bureau of Weights and Measures has ceased using the leap second. It is replaced by the leap hour whenever UTC wanders by that much. The first leap hour may occur in a few thousand years.