The 2016 leap second will take place at exactly 23:59:60 UTC on Dec 31, 2016. I’d advise system administrators to monitor processes during this time and pay extra attention to systems for a short while, especially if your system is busy running during that time range.
What’s a leap second, and why do we use it?
A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC) in order to keep its time of day close to the mean solar time, or UT1. Without such a correction, time reckoned by Earth’s rotation drifts away from atomic time because of irregularities in the Earth’s rate of rotation. Since this system of correction was implemented in 1972, 26 leap seconds have been inserted, the most recent on June 30, 2015 at 23:59:60 UTC, and the next leap second will be inserted on December 31, 2016, at 23:59:60 UTC.
And why the leap second matters?
Well basically it has the potential to crash your systems and applications (and here). To have the system properly handle the leap second, the system needs either to use time synchronization service like NTP or PTP, or have the tzdata package updated to the version which includes the change.
Redhat created a knowledgable article about the leap second handling, refer to Resolve Leap Second Issues in Red Hat Enterprise Linux for more details.