The arrow of time is the reason why random bits of shrapnel and chemicals don't fly together and "un-detonate" to become hand grenades. In one direction of time, entropy in the universe always increases; in the other, it always decreases. The question is, why?
The reason is very simple. Entropy is a measure of the probability of a particular outcome. The statement that "entropy increases" is simply the statement that the most probable thing to do happen is almost always the one that does happen. The "almost always" is a fantastically high probability. For example if I through a 1 cm cube of of aluminium at 26 C into a lake where the water is at a temperature of 25 C, there is something like a 10 ^-(10 ^10^23) chance that heat will from the lake into the aluminium cube and cause it's temperature to rise. If it did this the entropy of the Universe would decrease.
What this experiment observed is profound and extremely interesting. For some reason that isn't known, the Universe prefers that certain microscopic and reversible processes occur with a greater probability if time increases.
In other words there truly is a preferred direction to time which independent of tautology that the Universe is constantly evolving into a more probable state.
Actually this result is was first observed in K-mesons but this new result in B-mesons has much greater significance and confirms the previous observation.