The British author E.M. Forster introduced the influential terms "round" and "flat" for characters in his book "Aspects of the Novel" (1927).
According to the Penguin Dictionary of Literary Terms and Literary Theory, the essential distinction between round and flat characters is that a round character develops and changes in the course of a story or play, while a flat one stays the same.
The round character has further dimensions of her personality that are revealed as events in the story demand them. Forster said the test of a round character was whether he was able to convincingly surprise the reader.
Some authors favor one type of character, while others use both in the same work. In Shakespeare's Henry IV, Prince Hal is a round character (he changes) and Hotspur is a flat character.
Flat characters may be better-suited to some genres than others. Forster admired the flat characters of Charles Dickens and said that flat characters are best when they are comic.
Round characters are often considered superior to flat characters, but flat secondary characters can be useful. By contrasting Hal with Hotspur, Shakespeare makes his protagonist seem even more lifelike.