A second here, a second there. An it all adds up, as the International Telecommunications Union (ICU) votes to abolish the 'Leap Second'. (Leap second could be abolished - The Telegraph, 11 January 2012).
The Leap Second is truly an invention of the Digital World. It was introduced in concept in 1958, when it was accepted that Co-ordinated Universal Time (based in Atomic clocks - Cesium 132) would gradually differ from Astronomical time (based on the rotation of the Earth). The reason for this is the gradual slow down in the rotation of the Earth, by an approximate 2 thousandth's of a second per day. This would result in the two measures of time differing by an extra second every 500 days.
In 1958 the two times were set to be equal, and the first Leap second was added in 1972 and 23 have been added subsequently. The next is scheduled to be added at the end of June 2012. At present personal computers and the like do not accomodate 'Leap seconds' as they are not predicted and formalised as Leap years are:- they are decreed as and when the ICU sees fit.
But what is the imporatnce of these little times? To the man in the street, very little. Every so often you would need to change the time - by a second - if your watch, computer or cell phone was that accurate in the first place. But it is crucial to GPS systems. GPS transmitters and spatial calculators need precise timing to give the location - in the similar way that accurate watches became so important to seafarers in the 18th century (See for example, the book - 'Longitude' by Dava Sobel, on the importance of time to travellers). The military, in particular, use accurate GPS to control drones and missiles:- a second difference could be literally a life or death situation.
So at the end of June 2012, we MAY see time written for just a second, as 23:59:60 before clicking over to mi9dnight.