According to Wikipedia, the arrow of time is a term coined by British astronomer Arthur Eddington to distinguish between two types of physical processes:
Physical processes at the microscopic level are believed to be either entirely or mostly time symmetric, meaning that the theoretical statements that describe them remain true if the direction of time is reversed; yet when we describe things at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time. An arrow of time is anything that exhibits such time-asymmetry.
Put another way:
Any process that happens regularly in the forward direction of time but rarely or never in the opposite direction, such as entropy increasing in an isolated system, defines what physicists call an arrow of time in nature.
There are also some helpful rules about the arrow of time:
1) It is vividly recognized by consciousness.
2) It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.
3) It makes no appearance in physical science except in the study of organization of a number of individuals.
More on the arrow of time, including a great interview with Caltech theoretical physicist Sean Carroll, here at The Long Now Blog.

















