David Yerle

No, entropy does not explain the arrow of time. Entropy is a quantity which can be defined with the help of statistical mechanics. It is the logarithm of the number of microstates (the position and velocity of each particle in a system) compatible with a macrostate (the state you observe). For example, a gas at a certain temperature has millions of microstates which give the same macroscopic characteristics you observe. Entropy increases with time because greater number of microstates means greater probability. Therefore, when we say Entropy increases all we're saying is things tend to evolve to a more likely configuration, which is pretty obvious. There's nothing in the microscopic laws of physics that forces entropy to increase. For all we know, we could be going from future to past and we would never realize, as long as entropy increased in that direction. In this sense, increasing entropy means going towards the future. However, the question still remains: why is entropy so much larger in one extreme of time than in the other? For a better an longer explanation of this, check Sean Carroll's blog preposterous universe or read his book From Eternity to Here.