Although this short short story is called "Half a Day," it really spans a lifetime. In the first part of the story, we are told in vivid detail of a boy being walked by his father to his first day of school. We see what the boy is wearing and hear the words of wisdom the father offers about the importance of schooling.
Once there, events seem to blur into more than one day. We learn that:
It was not all a matter of playing and fooling around. Rivalries could bring about pain and hatred or give rise to fighting. And while the lady would sometimes smile, she would often scowl and scold. Even more frequently she would resort to physical punishment.
Is this one day or series of school days?
At the end of the first half day—or a series of days—the boy is let out of school and awaits his father, but no father comes. The city is also changed, bigger, more crowded, and more noisy. At the end of the story, the school boy is greeted as "grandpa."
The story is an allegory of life. Life takes years to live, day by day, but once you get older, it seems as is if it went by in a flash. Despite the reality of decades of physical time, the first day of school can remain a vivid memory that seems like yesterday and as if all the intervening years never happened. This is what the old man is experiencing. This is what all of us experience from time to time once we get to a certain age—and we don't have to be very old for this to occur. Even a teenager can look back at a childhood memory that feels like yesterday. Time is not as simple as it seems, and this story conveys that truth.