The play "The Hour of Truth" is titled quite accurately. There are several instances in the play where the truth of a person or a situation comes up, changing the perspective of the audience more than once.
When someone refers to "the hour of truth" in casual conversation, what is really meant behind the saying is that something will happen that will force a person come out just as he or she is, hence, a truth will be exposed.
It is arguable that, perhaps, the hour of truth comes when Mr. Baldwin refuses Mr. Gresham's offer and decides to testify in court everything he knows about the case- which is not a lot. This is truly "the hour of truth" because it shows us Mr. Baldwin as someone so true to his morals and integrity that he is capable of taking risks as big as those to preserve his dignity.
As a result, his hour of truth came with a great reward, which was a recommendation for a new job. He certainly shows the morale of the story: Lying does not pay.