You mean why it matters that we have leap seconds (it doesn't and they should be abolished) or why the news of it matters (because a 1000 crappy time implementations are going to walk off the end of buffers and do weird things) ?
Really it doesn't - people just have this attachment to days and the sun for telling the time.
The only people that a leap second realistically affects are astronomers and they are more than capable of managing their own time software.
At roughly 1 second every 1.5 - 2 years it will be a couple of millenia before the sun even gets an hour away from local noon - and people manage with daylight savings time.
So every 2000years we might need to introduce a leap hour.
It's even worse than that, because solar noon is already different from local noon almost always, almost everywhere.
First, you have to be precisely in the middle of a timezone, and not one of those weird timezones that doesn't actually follow the lines of longitude, either. Otherwise you're skewed late or early relative to solar time. Secondly, solar noon even at the precise center of timezones is only local 12:00 on average, because the timing of solar noon vis-a-vis a 24-hour clock fluctuates through the year by up to 18 minutes. Two factors are involved: the Earth's orbit is slightly eccentric, and Earth's axis of rotation isn't precisely perpendicular to the plane of its orbit (http://en.wikipedia.org/wiki/Equation_of_time has details and a graph).
So all the leap seconds do is keep the average local noon, at precise centers of timezones, equal to solar noon.
Why was this down-voted? I agree with the poster, and as far as I see, I wake up and everyone's clock is 1 second wrong, why precisely should I give a frig about this and how is the world going to end or change due to the clock going from :59 to :00 instead of :60 or anything being a second out?
Picture yourself riding an elevator in a tall office building, when the clock strikes midnight. The elevator controller has its time synced via posix time. The controller schedules when to stop running the elevator motor by reckoning from its last known position and projecting forward according to its estimated speed. Normally this calculation is performed 10 times a second so it's a smooth transition.
But when the clock jumps back abruptly by 1.0 s, the controller gets confused. Its next control loop update cycle is now scheduled 1100 ms into the future instead of the normal 100 ms period. This delays the motor shutdown signal and even causes the controller to miss the top-of-position sensor. The elevator car slams into the roof of the building. The cable snaps and all passengers contemplate Einstein for 10 s as the elevator car freefalls to their certain doom.
Well they would have, except that cable elevators have had mechanical safeties for a backup system since the 19th century.
OK, so instead:
Picture yourself receiving life-saving radiation therapy, when the clock strikes midnight ...