Irony means something that is contrary to what one might expect. In the story "Preludes," the judge is described as being disliked by his community. He is also not a good husband, because he cheats on his wife and misuses money sent to buy medicine. The behavior of cheating on your wife goes counter to most moral codes and therefore is unexpected behavior for a judge to engage in. Likewise, judges are meant to uphold the law, and misusing money goes counter to that.

Being a judge is considered to be a position of great power; it is usually awarded to smart people who have studied for a long time and are experts in their field. Therefore, most judges are respected by their community. However, in this case, the judge is not respected; instead, he is disliked. This difference between how you would expect a judge to act and to be received and how the judge actually acts and is considered by his community is ironic.