Discover IERS, the International Earth Rotation and Reference Systems Service. This is the group that studies and monitors the earth's rotation and it has put out a notice this past July 2008 regarding the "leap second".
According to the document:
A positive leap second will be introduced at the end of December 2008. The sequence of dates of the UTC second markers will be:
2008 December 31, 23h 59m 59s
2008 December 31, 23h 59m 60s
2009 January 1, 0h 0m 0s
Leap seconds are needed to resync mean solar time with international atomic time. Essentially, the second had originally been determined to be 1/86400 of a mean solar day, which was ultimately determined by the rotation of the earth about its axis. This way of counting the second was poor because of the elongation of the mean solar day by 1.5 ms per century (according to Wikipedia). In 1986, it was redefined according to the annual revolution of the earth around the sun. In 1967, and since then, the second was again redefined to be determined by the oscillation of a Cesium-133 atom, which is a physical, more constant way of counting. The original way and the atomic way of counting had been in sync back in 1750 to 1892. But with the continuation of the slowing of the earth's rotation, the atomic clock had been slowed to match it, from 1961 to 1971.
This slowing of the atomic clock didn't work out too well.
In 1972, the atomic second was brought back to the 1967's value (from counting oscillations of a Cesium-133 atom, which never actually changed). In order to account for the difference between atomic time and mean solar time, leap seconds were introduced. They are usually added after June 30 or December 31.
The leap second of December 2008 will have been the 24th leap second in history. The previous leap second was added at the end of 2005.
Wikipedia, as always, has a lot more of the details.
Moral of the story? Be extra careful when you are counting down to the New Year this Wednesday.