Perhaps the best way to understand direct characterization is to look at it from the side of "indirect characterization." When the author of a work does not directly speak of a person's character, then characterization is done indirectly. I can be done indirectly through hints, the thoughts and opinions of others, a sequence of actions, etc. Direct characterization takes place when the author makes direct statements about the character. However, you must be careful here. If the narrator is an all-knowing one, then the characterization may be direct. But if the narrator has proved to be wrong, then the narrator may not be giving a direct characterization.
The best thing to do is to look at characterization from as many possibilities as you can.
An example of direct characterization in Of Mice and Men is when the narrator says: "Curly was quick and mean." (The reader does not have to make any conclusions because the author/narrator states the trait directly.)
Indirect characterization is when Curly shows us how insecure he is when he is threatened by Lennie's size. We are indirectly "shown" by the author through the characters thoughts, feelings, and actions and left to make our own conclusions.