An example of a flat character would be Mrs. Micawber in the Charles Dickens novel "David Copperfield," while a modern example would be Bruce the shark in the film "Finding Nemo." A literary character is considered flat when the character only has a simple personality and the writer does not give the reader enough information about the character.
Another example of a flat character could be seen in the film "Harry Potter and the Sorcerer's Stone" in the character of Filch. Filch is obsessed with catching students and with his cat. The readers do not learn anything else about Filch so he remains a one-dimensional or flat character.
Flat characters are unimportant characters when it comes to the rest of the story, however, they may play crucial or partial roles in plot points. The opposite of the flat character would be the round character.
A round character is a character who is complex. He or she is typically referred to as three-dimensional and is most often a leading character in the story. An example of a round character would be Hermione Granger in "Harry Potter and the Sorcerer's Stone." Hermione is a complex character and a character who grows emotionally and mentally throughout the story as her personality changes.