Assuming you mean a "reading day" as in a day set aside to read, there are a variety of activities that can be undertaken.
For some, it may be a day to visit the local library and check out a few books. Others might choose to stay home and catch up on reading material they have been meaning to get to.
Some may use the day to read aloud to their children, or perhaps teach them how to read. And still others might set the day aside to work on their own reading skills.
Whatever the activity, the goal is simply to set aside some time to relax and enjoy reading.