Direct characterization is when the narrator tells the reader something about a character. Indirect characterization is when the narrator shows the reader something about the character through the character’s actions, things the character says, or things other characters say.
An example of direct characterization is when the narrator specifically tells us what a character is like. Consider this example of direct characterization from A Christmas Carol, in which the narrator describes Ebenezer Scrooge.
Oh, …. Scrooge! a squeezing, wrenching, grasping, scraping, clutching, covetous old sinner! Hard and sharp as flint, from which no steel had ever struck out generous fire; secret, and self-contained, and solitary as an oyster (Stave 1)
In this case, the narrator is describing Scrooge colorfully, but still just describing what he is like: mean and miserly. Compare that to this later example of indirect characterization.
Two men come to visit Scrooge collecting money for the poor. Scrooge asks why the poor do not just go to the workhouses.
“Many can't go there; and many would rather die.”
“If they would rather die,” said Scrooge, “they had better do it, and decrease the surplus population. …”(Stave 1)
Scrooge demonstrates here that he does not care about people. He prefers that the poor die, rather than giving money to help them. This is an example of how Scrooge is mean and miserly, but it is an indirect characterization. Rather than tell us Scrooge is miserly, we see Scrooge being miserly (and mean).
A story or novel should really have more indirect characterization than direct characterization, because it is more interesting, involves the reader, and moves the plot along.