11:59:60
So I was listening to an astronomy podcast and they talked about the leap second. What?!? That got my attention. 
This is a leap year, so I know that we have a February 29 this year. That's because the earth's orbit is 365.242199 days, so we have to add an extra day every four years. (Like how I have those extra decimal places? Let me tell ya, I'm feeling like a mighty proud geek right now!)
But I sure haven't heard of a leap second before. Apparently the earth's rotation isn't exactly the same all the time. Earthquakes, melting of ice sheets, and unknown factors can cause the earth to rotate at slightly different speeds. Our time system was based on measuring the amount of time from the sun's zenith (high point) one day to the sun's zenith the next. That time is 24 hours, which is divided into 60 minutes per hour and 60 seconds per hour. 
Then along came some people who needed (or wanted?) to measure time more exactly, hence the atomic clock, which uses atoms and measures wavelengths to determine time. So now we have a problem with this ultra precise time measuring system not jiving with what the earth is actually doing. 
Some super-smart people decided that the thing to do would be to add (or subtract) a second when necessary. This year, we need to add a second. So at the end of June, instead of the clock going from 11:59:59 to 12:00:00, it will go from 11:59:59 to 11:59:60 to 12:00:00. 
Of course something like changing time is a little controversial, which you can read about here, along with a whole lot more info about leap seconds. It will take a little longer than a second to read, so you'll have to decide if it's worth the time we'll be gaining.