Since I have an extra second today thanks to the leap second being added at 23:60 Universal Coordinated Time (UTC) I thought I would use that time to explain what a leap second is. Ok, maybe I need more than a second...
A day here on Earth is 24 hours long right? Yes and no. There are a lot of different definitions for time, and I mean a LOT! I could totally geek out here (and I really really want to), but instead will just point you to the US Naval Observatory site (Naval Oceanography Portal) where many (but not all) the various systems of time are defined.
A leap second is needed to ensure that the time difference between International Atomic Time (TAI) time and the UT1 time does not grow too large. What are these two different time systems and why do we care if the differences between the two grow large?
TAI is base purely on the atomic clock, which keeps time very precisely by measuring the oscillation of the Caesium-133 atom. The atomic clock does this because the official definition of a "second" is:
the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom
Ok, so we know how we define and measure a second and that the atomic clock keeps track of International Atomic Time (TAI) by measuring the Caesium-133 atom. So what it UT1? UT1 is essentially a measure of time based on the actual rotational rate of the Earth with respect to the Sun. The Earth's actual rotational rate changes due to things like earthquakes, gravitational interactions with the Moon and post-glacial rebound (the rise of land masses that were depressed by ice sheets during the last ice age). Because UT1 changes due to slight variations in the Earth's rotational rate, the difference between the extremely constant TAI time (atomic time) and UT1 varies. For example, the difference over one year was 0.28 seconds in 2011, but only 0.02 seconds in 2001. On average the discrepancy between TAI and UT1 grows to about 1 second every 1.5 years. Once this difference reaches 0.9 seconds the International Earth Rotation and Reference System Service (IERS) officially adds a leap second on either the last day of June or the last day of December. A leap second is added only on very specific days so people that REALLY need to know when leap seconds are going to happen can plan ahead.
So who REALLY cares about this type of thing? Complex systems that must use exact timing in order to operate accurately use atomic time, but those system interact with and are used by people who look at the clock on their walls which use Universal Coordinated Time (UTC). So systems that schedule maneuvers and activities for spacecraft in orbit must take into account this difference and plan accordingly. Telecommunications systems also rely on precise timing and some of these systems actually have to be turned off for 1 second in order to keep all the systems in sync.
So unless you are a satellite operator or in charge of complex telecommunications systems the only way a leap second is going to impact your life today is if you challenge someone in a bar bet about what the longest calendar day of the year is and win a free beer.