Raymond Tallis at the website of the Institute of Art and Ideas:
While most philosophers of time would be content to abandon the notion that time “flows”, “passes” or “moves”, the idea that time has a “direction” is more adhesive. Insofar as it is a consequence of the conception of time as a fourth dimension on a par with the three of space, it should, like flow , etc be incompatible with it. After all, the spatial dimensions do not have a direction. Collectively the spatial dimensions are the possibility of direction, just as they are the possibility of movement. Clearly, the direction of time – or the possibility of its having a direction – could not be provided by space. It would not make sense to say that time was pointing from left to right or up and down.
But there is something else, which is absolutely central; namely that the unfolding of time appears to be one way. This is in contrast to any direction in space – or any line marking a direction or trajectory in space. The line from A to B is also from B to A; any path going from a lower point to a higher point is also a path going from a higher point to a lower point. The apparent absence of this reversibility is all that there is to the direction of time. The link between earlier time t1 and later time t2 can be traversed in one direction- earlier-to-later – but not in the other direction – later-to-earlier. The path from t1 to t2 is inescapable while the path from t2 to t1 is blocked.
The hunt has therefore been on for something that will give time a direction in this very restricted sense of moving “forward” but not “backward”. This something will account for the difference between time and its spatial companions, a difference that will account for the fact that we can wander at will in space but not in time.