After June 30, 2015 if you have NTP or PTP time synchronization services installed in your Linux system, you'll see a kernel log like that:
Clock: inserting leap second 23:59:60 UTC
This is normal because of the extra leap second issue. It exists because the rotation of the earth is not very constant and varies a bit over time, while decreasing the mean rotation speed slowly.
Coordinated Universal Time (UTC) is derived from 250+ atomic clocks distributed in several countries. Main function of these atomic clocks is measuring the transition of energy levels in an atom to calculate UTC, and as this time measuring mechanism is independent of the Earth periodically the two must be brought into alignment with a leap second.
If you have a Linux kernel before the year 2013, you may have several problems after leap second adjustment. It is related to hrtimers in kernel and described detailly in the https://lwn.net/Articles/504744/ article. If you have such a system, it is strongly advised to upgrade your kernel to newer versions.