It was on this date in 1972 that the first leap second was added to a day.
The modern definition of a "second" was settled in 1874 by European scientists working from Muslim scholars' improvement on Ptolemy's Second Century calculations. But in the early 1960s astronomers realized that the rotation of the earth is irregular — fundamentally, it is slowing.
Coordinated Universal Time (CUT), calculated with an atomic clock, was systematically slowed each year, for a decade, to compensate. But that meant that CUT and UTC (the time standard used by broadcasters, transportation providers, and other commercial and military users, a standard still fixed on the original definition of the "second") were diverging. To true them up, the leap second was added to the UTC.
Since 1972, a total of 25 seconds have been added — that's to say, the Earth has slowed down 25 seconds compared to atomic time since then.
But this does not mean that days are 25 seconds longer nowadays: only the days on which the leap seconds are inserted have 86,401 instead of the usual 86,400 seconds.